Derive the expected value of Y? Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 36E
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A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in
years is given by
(ye 10
f(y)
0<y< 0⁰
100'
0,
elsewhere
Derive the expected value of Y?
Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be
a constant.
i) Find the moment generating function of X = -cY.
ii) What is the distribution of X?
Transcribed Image Text:A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by (ye 10 f(y) 0<y< 0⁰ 100' 0, elsewhere Derive the expected value of Y? Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X?
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