PROBABILITY THEORY Let X and Y be independent random variables with gamma distributions,r(3,2) and (4,2), respectively. The moment generating function of X andY arere (₁-2) and (₁-2) + + < 1/11-2t2ta)b)c)d)<<, respectively.2Calculate E(3X + 2Y + 1).Calculate Var(3x + 2Y+1).Obtain the distribution of W=X+Y.Compute E

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 21E

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PROBABILITY THEORY

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

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Let X and Y be independent random variables with gamma distributions, T(3,2) and (4,2), respectively. The moment generating function of X and Y are a) b) c) (₁2) and (2).<, respectively. - 2t -2t Calculate E(3X + 2Y+1). Calculate Var (3X + 2Y+1). Obtain the distribution of W=X+Y.

PROBABILITY THEORY