Suppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) = 2β. Further, suppose that given X = x , the RV Y has the Unif (0, x) distribution.a) Write down the conditional pdf of Y given X = x (f_Y|X )(y | x) =b) Find the joint pdf of (X,Y) (f_XY)(x,y)=c) Find the conditional mean and variance of Y E(Y | X=x) =____________ V(Y |X=x )= ____________d) Find the unconditional mean and variance of Y E( Y)= ____________ V(Y ) =____________e) Find the marginal pdf of Y (f_y)( y)= ___________f) Identify the distribution of Y Y-_________ g) Use parts e)- f) to find mean and variance of Y E(Y )=____________ V( Y)= ___________The answer forIs 1/x (0<y<x)Β2x/2 , (x2)/2β , βplease solve e) and f) and g) Beta >0Suppose that that the RV X has the Gamma (2, 3) distribution for some X>0, E(X)=28and V(X) = 2/3². Further, suppose that given X = x, the RV Y has the Unif (0, x)distribution.a)Write down the conditional pdf of Y given X = xSnx (y|x)=b) Find the joint pdf of (X,Y)fx (x, y) =c) Find the conditional mean and variance of YE(Y|X=x)=d)Find the unconditional mean and variance of YV(Y) =E(Y) =e) Find the marginal pdf of Yfy(y) =V(Y|X=x)=Identify the distribution of Y Y-g) Use parts e)- f) to find mean and variance of YE(Y) =V(Y)=

Given that the RV X has the distribution for some , and .Given , the RV Y has the distribution.

Answered: Suppose that that the RV X has the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Suppose that that the RV X has the Gamma(2,β ) distribution for some β > = 0, E(X) = 2β and V (X) = 2β. Further, suppose that given X = x , the RV Y has the Unif (0, x) distribution.

a) Write down the conditional pdf of Y given X = x (f_Y|X )(y | x) =
b) Find the joint pdf of (X,Y) (f_XY)(x,y)=
c) Find the conditional mean and variance of Y E(Y | X=x) =____________ V(Y |X=x )= ____________
d) Find the unconditional mean and variance of Y E( Y)= ____________ V(Y ) =____________
e) Find the marginal pdf of Y (f_y)( y)= ___________
f) Identify the distribution of Y Y-_________ g) Use parts e)- f) to find mean and variance of Y E(Y )=____________ V( Y)= ___________

The answer for

Is 1/x (0<y<x)
Β²
x/2 , (x²)/2
β , β

please solve e) and f) and g)

Beta >0
Suppose that that the RV X has the Gamma (2, 3) distribution for some X>0, E(X)=28
and V(X) = 2/3². Further, suppose that given X = x, the RV Y has the Unif (0, x)
distribution.
a)
Write down the conditional pdf of Y given X = x
Snx (y|x)=
b) Find the joint pdf of (X,Y)
fx (x, y) =
c) Find the conditional mean and variance of Y
E(Y|X=x)=
d)
Find the unconditional mean and variance of Y
V(Y) =
E(Y) =
e) Find the marginal pdf of Y
fy(y) =
V(Y|X=x)=
Identify the distribution of Y Y-
g) Use parts e)- f) to find mean and variance of Y
E(Y) =
V(Y)=

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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