The MLE’s of the means of X and Y in a bivariate normal distribution, given the variances of X and Y and the correlation between X and Y, can be found by solving the equations ∑(Xn-µx)/σx2 = 0 and ∑(Yn-µy)/σy2 = 0 for µx and µy. The solutions are µx = (1/n)∑Xn and µy = (1/n)∑Yn.
Let µx and µy be the means of X and Y, respectively.
The MLE of µx and µy can be found by maximizing the joint likelihood function:
L(µx, µy) = (2πσxσy√(1-ρ2))-n/2 exp{-1/2[∑(Xn-µx)2/σx2 + ∑(Yn-µy)2/σy2 - 2ρ(∑(Xn-µx)(Yn-µy)/(σxσy))]}
Taking the partial derivatives of L with respect to µx and µy and setting them to zero yields the equations
∑(Xn-µx)/σx2 = 0
∑(Yn-µy)/σy2 = 0
Solving these equations yields the MLE’s of µx and µy:
µx = (1/n)∑Xn
µy = (1/n)∑Yn
The MLE’s of the means of X and Y in a bivariate normal distribution, given the variances of X and Y and the correlation between X and Y, can be found by solving the equations ∑(Xn-µx)/σx2 = 0 and ∑(Yn-µy)/σy2 = 0 for µx and µy. The solutions are µx = (1/n)∑Xn and µy = (1/n)∑Yn.
The complete question is :
Suppose that the two-dimensional vectors (X1, Y1), (X2, Y2),. , (Xn, Yn) form a random sample from a bivariate normal distribution for which the means of X and Y are unknown but the variances of X and Y and the correlation between X and Y are known. Find the M. L. E. ’s of the means of X and Y.
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mother plays that you can in the oven when the clock in the dining room shows 10 minute past 7:00 the clock is 15 minutes fast the chicken will take 45 minutes to get ready. what will be the actual time when it is finished?
40 minutes past 7:00 is the actual time when the chicken will get ready.
What is the use of clock?The tool used to measure and indicate time is a clock or timepiece. The clock, one of the earliest creations by humans, satisfies the need to measure time periods that are shorter than those represented by natural units like the day, lunar month, and year. Over thousands of years, several physical processes have been utilized by devices.
The following examples of clocks that are based on movement in nature could be regarded forerunners of the modern timepiece: Through the positioning of a shadow on a flat surface, a sundial displays the time.
The hourglass is a well-known illustration of the variety of duration timers available. The two possible oldest clocks used to measure time are sundials and water clocks.
In Europe, the earliest mechanical clocks that kept time with oscillating timekeepers such balance wheels were made possible around 1300 thanks to the development of the verge escapement, which was a significant advancement.
Given the current time is 10 minute past 7:00, i.e. 7:10
But the clock is 15 min faster the original time
Original time = 7:10 - 15 min
= 6:55
And given time for the chicken to get ready is 45 min
Adding 45 min
= 6:55 + 45 min
= 7:40
Thus, 40 minutes past 7:00 is the actual time when the chicken will get ready.
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In TrIangle ABC, a = 11 cm, b = 14 cm, and m^C = 73 degrees. Use the Law of Cosines to determine c to
the nearest tenth of a centimeter.
Using the Law of Cosines the value of c is approx 15 cm.
In the given question, in ∠ABC, a = 11 cm, b = 14 cm, and m∠C = 73 degrees. Use the Law of Cosines we have to determine c to the nearest tenth of a centimeter.
The law of cosines in trigonometry establishes a relationship between a triangle's side lengths and the cosine of one of its angles.
The formula of Law of Cosines is
[tex]{\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \gamma ,}[/tex]
Now putting the value in the formula
[tex]c^{2}=(11)^{2}+(14)^{2}-2\times11\times14\times\cos73[/tex]
Now solving,
[tex]c^{2}[/tex] = 121+196-308×0.29
[tex]c^{2}[/tex] = 317-89.32
[tex]c^{2}[/tex] = 227.68
Taking square root on both side
c = 15.09
c = 15 (approx)
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What happens to the parent graph y= square root of X when the equation is changed to y=-2 square root of x-8 select all that apply.
Shift down 8 units, vertical stretch, reflect over the x-axis, shift up 8 units
Answer:
All except shift up.
pythagorean theorem word problems worksheet with answers
According to the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs of a right triangle.
In other words, [tex]a^2 + b^2 = c^2[/tex] for the triangle depicted below.
The right triangle's legs, a and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.
Construction projects and almost anything involving right triangles, such as roofing for homes, are common uses for this application.
Hypotenuse² = Base² + Perpendicular²
The Pythagorean Theorem is used in a variety of computations. For instance, it may be used to determine the height and distance of straight and fallen trees, as well as the steepness of hills and mountains.
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How do you write the domain and range of an exponential function?
All real numbers make up the domain, and all positive real numbers, or (0, ∞) in interval notation, make up the range.
Range and DomainThe domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in. They are the y values.
Exponential FunctionAn exponential function is a mathematical function of the following form: f ( x ) = ax. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828
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The table shows the number of grapes, y, and the number of strawberries, ×, in fruit salad. How many grapes would you need in fruit salad with 10 strawberries?
Answer: 40
Step-by-step explanation: y=4x so if there is 10 strawberries the 10x4=40 so there would need to be 40 grapes to make a fruit salad.
Which of the following best described the line that is passing through the ordered pairs given below? Select all that apply
(-4, 6) & (-4, 1)
The slope of the line is undefined.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (-4, 6) and (-4, 1)
Now,
Since, The equation of line passes through the points (-4, 6) and (-4, 1)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (1 - 6) / (-4 - (-3))
m = - 5 / 0
m = ∞
Thus, The slope of the line is undefined.
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In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3. 06 per gallon according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0. 06 per gallon to answer the following. A. What percentage of gasoline stations had prices within 3 standard deviations of the mean? b. What percentage of gasoline stations had prices within 2. 5 standard deviations of the mean? What are the gasoline prices within 2. 5 standard deviations of the mean? c. What percentage of gasoline stations had prices between $2. 94 and $3. 18
If the average price of regular unleaded gasoline excluding taxes was $3.06 per gallon then the percentage of gasoline stations had prices within 3 standard deviations of the mean is 99.74% .
The Average Price of the gasoline (μ) is = $3.06 per gallon ;
the standard deviation price per gallon (σ) is = 0.06 ;
we have to find the percent of gasoline that had prices within 3 standard deviations of the mean ;
the the 3 standard deviation is calculated by :
⇒ [tex](\mu \pm 3\sigma )[/tex]
On substituting the values ,
we get ;
⇒ [tex](\mu - 3\sigma , \mu +3\sigma)[/tex]
⇒ [tex](3.06 - 3\times 0.06 , 3.06 + 3\times 0.06)[/tex]
= (2.88 , 3.24) ;
Step two ;
Now , We have to calculate P(2.88 < X < 3.24)
= [tex]P(\frac{2.88-3.06}{0.06} < Z < \frac{3.24-3.06}{0.06} )[/tex]
= [tex]P(-3 < z < 3) ;\\[/tex]
which means , [tex]P(z < 3) - P(Z < -3)[/tex] ;
= 0.9987 - 0.0013 ;
= 0.9974 ≈ 99.74% .
Therefore , the required percent of gasoline is 99.74% .
The given question is incomplete , the complete question is
In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3. 06 per gallon according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon .
What percentage of gasoline stations had prices within 3 standard deviations of the mean ?
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What is the line xy pass through origin?
A line in the xy-plane passes through the origin and has a slope of 1/7 is 7y = x.
In the given question, we have to find a line in the xy-plane passes through the origin and has a slope of 1/7.
The equation of the line is:
y - y(1) = m(x - x(1))
The given points is (0, 0). So
x(1) = 0 and y(1) = 0
From the given question, m = 1/7
Now putting the value in the equation of line
y - 0 = 1/7(x - 0)
y = 1/7 x
Multiply by 7 on both side, we get
7y = x
Hence, a line in the xy-plane passes through the origin and has a slope of 1/7 is 7y = x.
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The complete question is:
What is a line in the xy-plane passes through the origin and has a slope of 1/7?
Construct the graph of the direct proportion y=kx for each value of k k=3x
the answer is 3x²
Step-by-step explanation:
we know that k = 3x
when we look at the actual equasion we can se that y = kx, meaning we have to multiply x by 3x which would give us 3x²
Answer: the answer is 3x^2 three x to the power of 2
In the diagram AB=BC
Prove that ABCD is a cyclic quadrilateral
Give reasons for any statements you make.
Answer:
Step-by-step explanation:
A quadrilateral is cyclic if and only if the opposite angles are supplementary, or add up to 180 degrees. Angle ABC is equal to angle BCD in the diagram because they are opposing angles of a parallelogram.
Furthermore, because AB=BC, the opposite angles are congruent, which implies they are equal. Because angle ABC equals angle BCD, angle ABC Plus angle BCD equals 180 degrees. As a result, we may deduce that ABCD is a cyclic quadrilateral.
Another technique to demonstrate that ABCD is a cyclic quadrilateral is to use the theorem "In a parallelogram, opposite sides and opposite angles are equal."
A parallelogram has equal opposed sides and equal opposite angles. We know that AB=BC in this situation, thus AB and BC are opposing sides, implying that the quadrilateral is a parallelogram. And because the opposite angles are equal, the quadrilateral is cyclic.
As a result, the congruence of parallel sides and opposing angles establishes that the quadrilateral is a cyclic quadrilateral.
• 51.) PROOF Prove that a median of an equilateral triangle is also an angle bisector, perpendicular bisector, and
altitude. [Hint: Sketch and label a picture.]
I
The medians from a vertex, altitudes, and angle bisectors all coincide for an equilateral triangle. As a result, an equilateral triangle has the same orthocenter O, centroid G, and incenter I.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
The medians from a vertex, altitudes, and angle bisectors all coincide for an equilateral triangle.
As a result, an equilateral triangle has the same orthocenter O, centroid G, and incenter I.
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susi is making stickers from 2 sheets of sticker paper, each sticker uses 1/16 of a sheet. what is the greatest number of stickers susi can make with 2 sheets of sticker paper
The greatest number of stickers Susi can make with 2 sheets of sticker paper is 128.
What is a fraction?
A fraction is a way of representing a part of a whole or a ratio of two numbers. It is written as a ratio of two numbers, called the numerator and the denominator, separated by a horizontal line or a slash.
Each sheet of sticker paper can be used to make 1/16 of a sheet of stickers, so two sheets of sticker paper can be used to make 2 * (1/16) = 2/16 = 1/8 of a sheet of stickers.
Since a sticker uses 1/16 of a sheet, the greatest number of stickers Susi can make from 2 sheets of sticker paper is 1/8 * (1/1/16) = 8 * 16 = 128 stickers.
Hence, the greatest number of stickers Susi can make with 2 sheets of sticker paper is 128.
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Question 2(Multiple Choice Worth 2 points)
(03.06 MC)
C
X
B
W D
y
What expression represents the value of y?
Oy=√xv
Oy = √wz
N
V
A
On solving the provided question, we can say that the expression of the triangle will be as follows = y = [tex]\sqrt{xy}[/tex]
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
here, the expression of the triangle will be as follows
y = [tex]\sqrt{xy}[/tex]
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A car starts at rest. after 4 seconds it is going 24 m/s. what was the car's acceleration?
The solution indicates that the car accelerates to 24 m/s, or 5 m/s, after 4 seconds.
what is acceleration?The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.
what is acceleration, and what is its unit?The rate at which an object's velocity varies with respect to time is known as acceleration in physics. Newton's Second Law states that an object's acceleration is the combined effect of all forces acting on it. The metre per second squared (m s2) unit of acceleration in the SI is used.
According to the given information:Acceleration = [tex]\frac{(Final velocity) - (initial velocity)}{time}[/tex]
Acceleration = (20 - 0) / 4
= 5m/s
According to the solving the car's acceleration = 5m/s.
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1\2 y= 1 in standard form
Answer:
y=2
Step-by-step explanation:
How many real solutions does the system of equations have?
It is occasionally possible for a system of linear equations to have an infinite solution (the same line) or no solutions (parallel lines), most systems only have one solution.
What exactly are equational systems?In algebra, multiple equations that must be solved simultaneously (the solution must satisfy all of the system's equations) are referred to as simultaneous equations or systems of equations. A system must have an equal number of equations and unknowns for it to have a singular solution. Even then, a solution is not guaranteed.
When there is sufficient information to formulate equations for multiple unknowns, systems of equations are utilized for problem solving.
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True or False: The first equation can be algebraically manipulated into the second equation. (in
other words, the two equations are equivalent)
1st: 6x +2=-20
2nd: 6x +22=0
o True
O False
Answer: False.
Step-by-step explanation: The two equations are not equivalent because the constant terms on the right side of each equation are different. The first equation has -20 on the right side, while the second equation has 0 on the right side. The equations cannot be manipulated into each other because the constant terms are different.
Gregory's Motors has motorcycles (two wheels)
and ATVs (four wheels) in stock. The store has 45
vehicles, that together, have 130 wheels.
Let y represent the motorcycles and x represent
the ATVS.
a. Write an equation for the number of motorcycles and
ATV:
b. Write an equation for the total number of wheels:
*****
CO
KEEP
Submit
c. Solve the
Number of Motorcycles
504
45-
-40-
-35-
-30
25-
20
15
The equation that represent the total number of vehicles is x + y = 45
The equation that represent the total number of wheels is 4x + 2 y = 130
The total number of motocycles are 25 and number of ATVs are 20.
What are Linear Equations ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
A linear equation is expressed using the linear equation formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form.
Let y represent the motorcycles and x represent
The equation that represent the total number of vehicles is
x + y = 45 (i)
The equation that represent the total number of wheels is
4x + 2 y = 130
⇒ 2x + y = 65 (ii)
Subtracting equation (i) from (ii) we get ,
2x + y - x - y = 65 - 45
x = 20
putting x = 20 in equation (i) we get
y = 45 - 20 = 25
The total number of motocycles are 25 and number of ATVs are 20.
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Select the graph of the solution. Click until the correct graph appears.
| x | + 3 > 7
The inequality can be rewritten into:
x > 4 or x < -4
And the graph can be seen in the image at the end.
How to solve the inequality?We want to solve the inequality below and then graph it, the inequality is:
|x| + 3 > 7
moving the 3 to the right side we get:
|x| > 7 - 3
|x| > 4
Now we can break the absolute value part into two:
x > 4
x < -4
That is the solution:
x > 4 or x < -4
The graph is the one below.
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476.9 x 100?
Long multiplication with solution, needed ASAP! Thank you
Answer: 476.9 x 100 = 47690
Step-by-step explanation: When you multiply a number by 100, you are simply adding two zeroes to the end of the number.
So, for example, to find 476.9 x 100, you can simply add two zeroes to the end of 476.9, giving you 47690.
Another way to think about it is to move the decimal point 2 places to the right.
476.9 -> 476.90
Therefore 476.9 x 100 = 47690
A chef is estimating the cost to prepare a fixed-price menu for x guests. The anticipated cost of the appetizers is
a(x) = 3.25x, the anticipated cost for the main course is m(x) = 5.25x, and the anticipated cost for the dessert course is d(x) = 1.25x.
If the functions are combined so that
c(x) = a(x) + m(x) + d(x), then the function c(x) includes the point (40,
The cost function, c(x), includes the point (40, 390)
What is a function?A function is a rule that maps input variables to output variables, with each input producing exactly one output.
The cost functions the chef uses to estimate the cost of the fixed price menu for x guest are ppresented as follows;
The function for the anticipated cost of appetizers, a(x) = 3.25·x
The function for the anticipated cost for the main course, m(x) = 5.25·x
The cost function for the anticipated cost of the desert, d(x) = 1.25·x
The function for the combined function, which is the cost of the fixed price menue is therefore;
c(x) = a(x) + m(x) + d(x)
The po
The point included in the function, c(x) (40, can be found by plugging in the value, x = 40 in the cost function c(x) = a(x) + m(x) + d(x). as follows;
The point on the cost function is; (40, (c(40))
c(40) = a(40) + m(40) + d(40)
c(40) = 3.25 × 40 + 5.25 × 40 + 1.25 × 40 = 390
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How do you plot a negative graph?
Negative numbers are to the left of the origin on the x-axis and below the origin on the y-axis. To graph with negative numbers, start at the origin and go to the left if the x-value is negative, and downward if the y-coordinate is negative.
Now, According to the question:
Graph with Negative Numbers:
Graphing with negative numbers follows the same process as graphing with positive numbers, but the points will lay in quadrants II, III, and IV. Negative numbers are to the left of the origin on the x-axis and below the origin on the y-axis. To graph with negative numbers, start at the origin and go to the left if the x-value is negative, and downward if the y-coordinate is negative. Points in quadrant I will always follow the format (+, +). Points in quadrant II will be (-, +), points in quadrant III will be (-, -), and points in quadrant IV will be (+, -). The image below depicts four points graphed on the coordinate plane. Three of the points (green, blue, and purple) contain negative coordinates.
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Ten balls in five lines Puzzle – Solution The puzzle Place 10 balls in 5 rows in such a way that each row contains exactly 4 balls.
Ten balls in five lines Puzzle – Solution The puzzle Place 10 balls in 5 rows in such a way that each row contains exactly 4 balls below figures are:
A puzzle is a sport, trouble, or toy that examines a person's ingenuity or understanding. In a puzzle, the solver is anticipated to position pieces together (or take them aside) in a logical manner, so that you can arrive at the appropriate or a laugh solution to the puzzle. There are special genres of puzzles, which include crossword puzzles, phrase-search puzzles, variety puzzles, relational puzzles, and good judgment puzzles. the academic take look at puzzles is referred to as enigmatology.
Puzzles are often created to be a form of leisure however they can also get up from critical mathematical or logical problems. In such cases, their solution can be a substantial contribution to mathematical research. Puzzles expand memory competencies, as well as the capability to devise, check ideas and solve troubles. even as completing a puzzle, children want to recollect shapes, colors, positions, and techniques to complete them.
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Translate the equation P= IV into a sentence with the same meaning.
Give the unknowable quantity a variable in step 1. Let z be the undetermined number. Finding two verbal expressions with the same value is the second step. Use fractions when creating a mathematical equation from the phrase "quotient" Step four is to solve the equation.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. A mathematical expression known as an equation is one in which one side of the expression equals the other, as in the example above: Since we know that 4 + 4 = 8 and 10 - 2 = 8, the equation is true because both sides are equal.To learn more about equation refer to:
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Does anyone know what 354 times 781 is?
Answer:
It is 276474
Step-by-step explanation:
What is the formula of parabola graph?
The standard form of the equation of a parabola is y = ax² + bx + c, where 'a', 'b' and 'c' are constants.
A parabola is a type of curve in mathematics, and it is defined by an equation of the form y = ax² + bx + c. Here, a, b, and c are constants and x is a variable. The graph of this equation is a U-shaped curve, which is symmetrical about the line x = -b/(2a). The curve has exactly one point of inflection, located at -b/(2a), and the curve opens either up or down depending on the value of a. The vertex of the parabola also occurs at the point -b/(2a). Parabolas are used to describe a wide range of phenomena, including projectile motion and the trajectory of satellites in space. They are also used in optics, engineering, and other sciences.
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What is the distance of point A (- 5/6 from the origin?
The distance between the point (-5, 6) to the origin is 61 units.
What do we mean by distance?Regardless of direction, an object's distance is defined by its total velocity.
Distance is the amount of space an object has traveled, regardless of where it began or concluded.
Knowing an object's distance from us allows us to determine its true size.
The following formula is widely used to determine the distance between two points: d=((x2 - x1)2 + (y2 - y1)2)
The given point is thus:
(-5, 6)
Assume that (0, 0) serves as the origin and that the given position is at (-5, 6).
d=((-5 - x1)2 + (6 - y1)2)
d=((-5)2 + (6)2)
d=25+36
d=61 units
Therefore, the distance between the point (-5, 6) to the origin is 61 units.
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What is the value of log 7 base 343?
The value of log 7 base 343 is 1/3.
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base b is written as [tex]log_b (x)[/tex], [tex]log_b x[/tex], or even without the explicit base, log x.
[tex]log_{343}(7)[/tex] = x
Step1:Rewrite in exponential form first.
[tex]343^{x}[/tex] = 7
Step 2:Take the log from both sides .
log [tex]343^{x}[/tex] = log 7
Step 3: Use the log rule log [tex]a^x[/tex]=x log a
x log 343=log 7
x = log 7/log 343
Now use a calculator.
x = 1/3
The value of log 7 base 343 is 1/3.
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Question 1 pls answer
Answer: False
Step-by-step explanation:
The question asks for 3*1/3.
In this case, this can be translated as 3/3.
3 divided by 3 equals 1, not 9.
So the answer is False.