Consider two random variables with joint density fY1,Y2(y1,y2)
=(2(1−y2) 0 ≤ y1 ≤ c,0 ≤ y2 ≤ c 0 otherwise
(a) Find a value for c. (4 marks) (b) Derive the density function
of Z = Y1Y2. (10 marks)
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Consider two random variables with joint density fY1,Y2(y1,y2)
=(2(1−y2) 0 ≤ y1 ≤ c,0 ≤ y2...
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1,...
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2)...
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
Please Only Do Question 2 [1] The joint probability density function of two continuous random variables...
Please Only Do Question 2
[1] The joint probability density function of two continuous random variables X and Y is fxxx(x,y) = {S. sc, 0 <y s 2.y = x < 4-y otherwise Find the value of c and the correlation of X and Y. [2] Consider the same two random variables X and Y in problem [1] with the same joint probability density function. Find the mean value of Y when X<1.
If two random variables have the joint density (x + y2), for 0 < x <...
If two random variables have the joint density (x + y2), for 0 < x < 1, 0 < y < 1 0, elsewhere. find the probability that 0.2 < X < 0.5 and 0.4 <Y < 1.6. With reference to the previous Problem 6, find both marginal densities and use them to find the probabilities that a. X > 0.8; b. Y < 1.5.
The joint probability density function of two continuous random variables X and Y is Find the...
The
joint probability density function of two continuous random
variables X and Y is
Find the value
of c and the correlation of X and Y.
Consider the
same two random variables X and Y in problem [1] with the same
joint probability density function. Find the mean value of Y when
X<1.
fxy(x,y) = { C, 0 <y < 2.y < x < 4-y 10, otherwise
Let X. Y be two random variables with joint density fx.x(x,y) = 2(x + y), 0<x<y<1...
Let X. Y be two random variables with joint density fx.x(x,y) = 2(x + y), 0<x<y<1 = 0, OTHERWISE a) Find the density of Z = X-Y b) Find the conditional density of fXlY (x|y) c)Find E[X|Y (x|y)] d) Calculate Cov(X, Z)
Let Y1, Y2 have the joint density f(y1,y2) = 4y1y2 for 0 ≤ y1,y2 ≤ 1...
Let Y1, Y2 have the joint density f(y1,y2) = 4y1y2 for 0 ≤ y1,y2 ≤ 1 = 0 otherwise (a) (8 pts) Calculate Cov(Y1, Y2). (b) (3 pts) Are Y1 and Y2 are independent? Prove your answer rigorously. (c) (6 pts) Find the conditional mean E(Y2|Y1 = 1). 3
(2) Suppose the random variables Yi and Yg have joint probability density function (n 2)-10 The marginal distributions are fi (y) = y/2 for 0 yIS 2 (zero otherwise) and fn (Y2)-2-2y2 for 0 Y2 1 (zero...
(2) Suppose the random variables Yi and Yg have joint probability density function (n 2)-10 The marginal distributions are fi (y) = y/2 for 0 yIS 2 (zero otherwise) and fn (Y2)-2-2y2 for 0 Y2 1 (zero otherwise). (a) Calculate E(Y) and E(Y2) (b) Calculate the conditional densities of YilY2-/2 and Y2Y- (c) Derive ElYalyǐ-m] and EMM-Y21 (d) Calculate EIE(Y1Yİ)] and E [E(YĪ½j. and confirm your answers in (a). (e) Calculate E(YiYo) and compare it with E(Y)E(5).
(2) Suppose the...
Suppose two random variables Y1 and Y2 have the following quantities: E(Y) = 3, E(Y/2) =...
Suppose two random variables Y1 and Y2 have the following quantities: E(Y) = 3, E(Y/2) = 18, E(Y2) = 5, E(Y22) = 29, E(Y1Y2) = 11 Find the correlation coefficient of Y1 and Y2. That is to find the value of Corr(Y 1, Y2) -4.0000 0.6667 O -0.1111 -0.6667
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
Please Only Do Question 2
[1] The joint probability density function of two continuous random variables X and Y is fxxx(x,y) = {S. sc, 0 <y s 2.y = x < 4-y otherwise Find the value of c and the correlation of X and Y. [2] Consider the same two random variables X and Y in problem [1] with the same joint probability density function. Find the mean value of Y when X<1.
If two random variables have the joint density (x + y2), for 0 < x < 1, 0 < y < 1 0, elsewhere. find the probability that 0.2 < X < 0.5 and 0.4 <Y < 1.6. With reference to the previous Problem 6, find both marginal densities and use them to find the probabilities that a. X > 0.8; b. Y < 1.5.
The
joint probability density function of two continuous random
variables X and Y is
Find the value
of c and the correlation of X and Y.
Consider the
same two random variables X and Y in problem [1] with the same
joint probability density function. Find the mean value of Y when
X<1.
fxy(x,y) = { C, 0 <y < 2.y < x < 4-y 10, otherwise
Let X. Y be two random variables with joint density fx.x(x,y) = 2(x + y), 0<x<y<1 = 0, OTHERWISE a) Find the density of Z = X-Y b) Find the conditional density of fXlY (x|y) c)Find E[X|Y (x|y)] d) Calculate Cov(X, Z)
(2) Suppose the random variables Yi and Yg have joint probability density function (n 2)-10 The marginal distributions are fi (y) = y/2 for 0 yIS 2 (zero otherwise) and fn (Y2)-2-2y2 for 0 Y2 1 (zero otherwise). (a) Calculate E(Y) and E(Y2) (b) Calculate the conditional densities of YilY2-/2 and Y2Y- (c) Derive ElYalyǐ-m] and EMM-Y21 (d) Calculate EIE(Y1Yİ)] and E [E(YĪ½j. and confirm your answers in (a). (e) Calculate E(YiYo) and compare it with E(Y)E(5).
(2) Suppose the...
Suppose two random variables Y1 and Y2 have the following quantities: E(Y) = 3, E(Y/2) = 18, E(Y2) = 5, E(Y22) = 29, E(Y1Y2) = 11 Find the correlation coefficient of Y1 and Y2. That is to find the value of Corr(Y 1, Y2) -4.0000 0.6667 O -0.1111 -0.6667
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