4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2), respectively. The moment generating function of X and Y are *(1-2)' (1) and ().<. respectively. a) b) c) Calculate E(3X + 2Y+1). Calculate Var (3X + 2Y+1). Obtain the distribution of W = X+Y. (1)

4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2), respectively. The moment generating function of X and Y are *(1-2)' (1) and ().<. respectively. a) b) c) Calculate E(3X + 2Y+1). Calculate Var (3X + 2Y+1). Obtain the distribution of W = X+Y. (1)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

4.
Let X and Y be independent random variables with gamma distributions,
r(3,2) and I'(4,2), respectively. The moment generating function of X and
Y are
• (1-2₁)
a)
b)
c)
d)
and
¹ (1-2)* · · </
Calculate E(3X + 2Y+1).
Calculate Var (3X + 2Y + 1).
Compute E
, respectively.
Obtain the distribution of W = X+Y.
(+).

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