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Suppose y has a「(1,1) distribution while X given y has the conditional pdf elsewhere 0 Note that both the pdf of Y and the conditional pdf are easy to simulate. (a) Set up the following algorithm to...
2. X has pdf fx (+) = 3x I(0 <r <1) and Y has conditional distribution, given X = r, of Uniform(-1,2). a) Obt...
2. X has pdf fx (+) = 3x I(0 <r <1) and Y has conditional distribution, given X = r, of Uniform(-1,2). a) Obtain the pdf of X, Y. Sketch the support of this pdf. b) Obtain E(Y|X) and E(YPX). Also obtain E(XY|X) by using an appropriate property of conditional expectation and one of the previous two calculations c) Find Cov(X,Y), that is the covariance of X with Y. Are X and Y independent? Justify your answer. The next page...
0〈z,0〈y Given the following joint distributionfrY(x,y)-, cez+2y else Calculate the following 1. The value of c...
0〈z,0〈y Given the following joint distributionfrY(x,y)-, cez+2y else Calculate the following 1. The value of c that makesfxy a proper pdf 2. The marginal distribution function fx(z) 3. The marginal distribution function fy () 4. P(X 1) 7. The random variables X and Y are independent if it is possible to write fxy (x, y) as the product of Íx (x) and fy (y) such that/xy(z, y) = k . Íx (x) . fy(y) for some value of k. Are...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y)...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
The joint distribution of two continuous random variables X and Y are given by: [xx{xy) =...
The joint distribution of two continuous random variables X and Y are given by: [xx{xy) = Cry, for OSIS ys 1, and 0 elsewhere a) (2pt) Find C to make fxy(x,y) a valid probability density function. Enter the numerical value of C here: b) (2pt) What should be the correct PDF for x(x); 1. fx (I) = 2r for 0 5r31, and elsewhere. 2. fx(x) = 3-2 for 0 Sis 1 and 0 elsewhere. 3. fx (x) = 4r(1 –...
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make...
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
Suppose (X,Y ) is chosen according to the continuous uniform distribution on the triangle with vertices (0,0), (0,1) and (2,0), that is, the joint pdf of (X,Y ) is fX,Y (x,y) =c, for 0 ≤ x ≤ 2,0 ≤ y ≤...
Suppose (X,Y ) is chosen according to the continuous uniform distribution on the triangle with vertices (0,0), (0,1) and (2,0), that is, the joint pdf of (X,Y ) is fX,Y (x,y) =c, for 0 ≤ x ≤ 2,0 ≤ y ≤ 1, 1/ 2x + y ≤ 1, 0 , else. (a) Find the value of c. (b) Calculate the pdf, the mean and variance of X. (c) Calculate the pdf and the mean of Y . (d) Calculate the...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
please answer both question. Question 2. Suppose X has the following pdf, , otherwise Please answer...
please answer both
question.
Question 2. Suppose X has the following pdf, , otherwise Please answer the following questions. 1. Find the value of C that makes fx(x) a valid pdf. 2. Does X have a distribution? If so, ho many degrees of freedom? 3. What is the mean and the standard deviation of X? (No need to "derive" this. Use the result in your note.) . What is the mgf of X? (No need to "derive" this. Use the...
2. X has pdf fx (+) = 3x I(0 <r <1) and Y has conditional distribution, given X = r, of Uniform(-1,2). a) Obtain the pdf of X, Y. Sketch the support of this pdf. b) Obtain E(Y|X) and E(YPX). Also obtain E(XY|X) by using an appropriate property of conditional expectation and one of the previous two calculations c) Find Cov(X,Y), that is the covariance of X with Y. Are X and Y independent? Justify your answer. The next page...
0〈z,0〈y Given the following joint distributionfrY(x,y)-, cez+2y else Calculate the following 1. The value of c that makesfxy a proper pdf 2. The marginal distribution function fx(z) 3. The marginal distribution function fy () 4. P(X 1) 7. The random variables X and Y are independent if it is possible to write fxy (x, y) as the product of Íx (x) and fy (y) such that/xy(z, y) = k . Íx (x) . fy(y) for some value of k. Are...
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
The joint distribution of two continuous random variables X and Y are given by: [xx{xy) = Cry, for OSIS ys 1, and 0 elsewhere a) (2pt) Find C to make fxy(x,y) a valid probability density function. Enter the numerical value of C here: b) (2pt) What should be the correct PDF for x(x); 1. fx (I) = 2r for 0 5r31, and elsewhere. 2. fx(x) = 3-2 for 0 Sis 1 and 0 elsewhere. 3. fx (x) = 4r(1 –...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
please answer both
question.
Question 2. Suppose X has the following pdf, , otherwise Please answer the following questions. 1. Find the value of C that makes fx(x) a valid pdf. 2. Does X have a distribution? If so, ho many degrees of freedom? 3. What is the mean and the standard deviation of X? (No need to "derive" this. Use the result in your note.) . What is the mgf of X? (No need to "derive" this. Use the...
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