2. Moment Generating Functions Let X be a random variable with moment generating function 1 mx(t) = 8t 1 -2t 1 + 3 + -8t + 1 a) Use the derivatives of mx(t) to find the mean and variance of X. b) Find the probability mass function of X and use it to check your results for the mean and variance you derived in a).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 76E
Question

please solve it on paper 

2.
Moment Generating Functions
Let X be a random variable with moment generating function
1
mx(t)
=
8t
1
-2t
1
+
3
+
-8t
+
1
a) Use the derivatives of mx(t) to find the mean and variance of X.
b) Find the probability mass function of X and use it to check your results for the mean and
variance you derived in a).
Transcribed Image Text:2. Moment Generating Functions Let X be a random variable with moment generating function 1 mx(t) = 8t 1 -2t 1 + 3 + -8t + 1 a) Use the derivatives of mx(t) to find the mean and variance of X. b) Find the probability mass function of X and use it to check your results for the mean and variance you derived in a).
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