Question

A continuous r.v. X follows the pdf: ?(?) = 2? 3 when 1 ≤ ? ≤...

A continuous r.v. X follows the pdf: ?(?) = 2? 3 when 1 ≤ ? ≤ 2.

(a) Find the cdf of X for 1 ≤ ? ≤ 2.

(b) Find the mean and variance of X.

(c) Find P(X = 1.22)

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

The pdf of the random variable X is

a) By definition,

The cdf of X is given by

b) The mean of random variable X is

Moreover,

Hence,

The variance of X =

c) since X is a continuous variable.

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