**2.3.3.** Let $f(x_1, x_2) = 21x_1^2 x_2^3$, $0 < x_1 < x_2 < 1$, zero elsewhere, be the joint pdf of $X_1$ and $X_2$.**(a)** Find the conditional mean and variance of $X_1$, given $X_2 = x_2$, $0 < x_2 < 1$.**(b)** Find the distribution of $Y = E(X_1|X_2)$.**(c)** Determine $E(Y)$ and $\text{Var}(Y)$ and compare these to $E(X_1)$ and $\text{Var}(X_1)$, respectively.

Given f(x1,x2)=21x12x22 0<x1<x2<1

2.3.3. Let f(¤1, 2) = 21rf, 0 < 01 < ¢2 < 1, zero elsewhere, be the joint pdf of X1 and X2. (a) Find the conditional mean and variance of X1, given X2 = x2, 0 < T2 < 1. (b) Find the distribution of Y = E(X1|X2). (c) Determine E(Y) and Var(Y) and compare these to E(X1) and Var(X1), re- spectively.

2.3.3. Let f(¤1, 2) = 21rf, 0 < 01 < ¢2 < 1, zero elsewhere, be the joint pdf of X1 and X2. (a) Find the conditional mean and variance of X1, given X2 = x2, 0 < T2 < 1. (b) Find the distribution of Y = E(X1|X2). (c) Determine E(Y) and Var(Y) and compare these to E(X1) and Var(X1), re- spectively.

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

**2.3.3.** Let $f(x_1, x_2) = 21x_1^2 x_2^3$, $0 < x_1 < x_2 < 1$, zero elsewhere, be the joint pdf of $X_1$ and $X_2$.

**(a)** Find the conditional mean and variance of $X_1$, given $X_2 = x_2$, $0 < x_2 < 1$.

**(b)** Find the distribution of $Y = E(X_1|X_2)$.

**(c)** Determine $E(Y)$ and $\text{Var}(Y)$ and compare these to $E(X_1)$ and $\text{Var}(X_1)$, respectively.

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