The moment-generating function of a random variable X is given by M(t) = 0.2 +0.4e5t +0.1e20t +0.3e¹⁰t (a) Find the pmf of X. (b) Find the values of E(X+3) and o² for X.
The moment-generating function of a random variable X is given by M(t) = 0.2 +0.4e5t +0.1e20t +0.3e¹⁰t (a) Find the pmf of X. (b) Find the values of E(X+3) and o² for X.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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![The moment-generating function of a random variable X is given by
M(t) = 0.2 +0.4e5t +0.1e20t +0.3e¹0t
(a) Find the pmf of X.
(b) Find the values of E(X+3) and o² for X.
(c) Calculate P(X ≥ 2).
(d) Compute E(2X + 1), using a calculator or R to help with the calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3b2b977-49e2-428f-b276-1fc0022629e3%2Fbe4952fe-2372-46ab-a37b-de5749f5900d%2Fahiaov_processed.png&w=3840&q=75)
Transcribed Image Text:The moment-generating function of a random variable X is given by
M(t) = 0.2 +0.4e5t +0.1e20t +0.3e¹0t
(a) Find the pmf of X.
(b) Find the values of E(X+3) and o² for X.
(c) Calculate P(X ≥ 2).
(d) Compute E(2X + 1), using a calculator or R to help with the calculations.
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