Question 3: Suppose that X and Y are independent random variables, and that theirmoment generating functions are given by:1Мx(t) —1for t <1My(t) =for t <1– Ot(1 — ө€)3(a)Find var(X +Y)(Ъ)Find E(XY)

We will use moment generating function of gamma distribution.

Answered: Question 3: Suppose that X and Y are…

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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The joint PDF of two jointly continuous random variables X and Y is S c(x2 + y?) for 0 < x < 1 and 0 < y < 1, fx,x(x, y) ‚Y otherwise. c = 3/2. E(Y) = 5/8. 3(2X2 + 1) 4(3X² + 1)' Show that E(Y|X) :
The random variable X has the following moment generating function: Mx(t) = , t < 1. 1–t Find E(X) and Var(X). Select one: E(X)= 1/2, Var(X) = 3/10 E(X) = 0, Var(X) = 1 O E(X)= ∞, Var(X) = ∞ E(X) = 1, Var(X) = 1
We have a random variable X and Y that jave the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} If U = Y-X2 , what is the support for the random variable U? What would fu(u) and Fu(u) be? Say U = Y/X, what is the support for the random variable U? What would fu(u) and Fu(u) be?
2. A random variable X has the discrete uniform distribution f(x; k) = {6. elsewhere. x = 1, 2, ..., k, 0, k Show that the moment-generating function of X is e'(1 – ekt) k(1 – et) Mx(t) -

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Question 3: Suppose that X and Y are independent random variables, and that their moment generating functions are given by: 1 for t < 1 1 Mx(t) : My(t) = 1 for t < 1- Ot (1— өt)3 Find var(X +Y) Find E(XY) (a) (b)