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Quiz 5 Moment Generating functions - Probability and Statistics | STA 4442, Quizzes of Probability and Statistics
Material Type: Quiz; Professor: Niederhausen; Class: Probability and Statistics 1; Subject: Statistics; University: Florida Atlantic University; Term: Fall 2009;
Typology: Quizzes
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Prob&Stats 1 Quiz 5 10/9/
If the moment generating function of X is
M (t) =
e t^ +
e^2 t^ +
e^3 t;
Önd the p.m.f, the mean, and the variance of X. Find P (1 X 3). p.m.f.: p ( 1) = 1= 6 , p (2) = 1= 2 , p (3) = 1= 3 mean: 1 16 + 2 12 + 3 13 = 116 = 1: 833 33 E [X^2 ] = 1 16 + 4 12 + 9 13 = (^316) V ar [X] = 316
11
6
2
= 6536 = 1: 805 56
P (1 X 3) = p (2) + p (3) = 12 + 13 = 0:833 333