4. The moment-generating function of a random variable X is est – e4t M(t) t + 0, and M(0) = 1. 4t (a) Find E(X). (b) Find Var(X). (c) Find P(4.5 < X < 7.5).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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4. The moment-generating function of a random variable X is
e8t – e4t
M(t)
t + 0, and M(0) = 1.
4t
(a) Find E(X).
(b) Find Var(X).
(c) Find P(4.5 < X < 7.5).
Transcribed Image Text:4. The moment-generating function of a random variable X is e8t – e4t M(t) t + 0, and M(0) = 1. 4t (a) Find E(X). (b) Find Var(X). (c) Find P(4.5 < X < 7.5).
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