Question

Given f(x) = ( c(x + 1) if 1 < x < 3 0 else as...

Given
f(x) = (
c(x + 1) if 1 < x < 3
0 else
as a probability function for a continuous random variable; find
a. c.
b. The moment generating function MX(t).
c. Use MX(t) to find the variance and the standard deviation of X.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given the PDF

a) The condition for valid PDF is

b) The moment generating function (MGF) is

c) The expectation is

Applying L'Hospital' rule,

Similarly,

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