4.1. Suppose X and Y are independent random variables, which are jointly continuous.x' is equal to the distribution1. Show carefully that the distribution of 'X + Y given Xof the random variable à +Y.Hint: Consider the change of variables h(x, y) = (x,x+y).=2. Suppose X and Y each have an exponential distribution with parameter a, find the jointp.d.f of X and X + Y.3. In the situation of (ii) above calculate E[X | X + Y].

Suppose X and Y each have an exponential distribution with parameter .

Answered: 4.1. Suppose X and Y are independent…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3.3.24. Let X1, X2 be two independent random variables having gamma distribu- tions with parameters a₁ = 3, B₁ = 3 and a2 = 5, B2 = 1, respectively. (a) Find the mgf of Y = 2X₁ +6X2. (b) What is the distribution of Y?
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