Concept explainers
Find E[Y(Y − 1)] for a geometric random variable Y by finding
Find
Find the variance of Y.
Answer to Problem 85E
The value of
The variance of Y is
Explanation of Solution
Calculation:
The geometric random variable Y has the probability distribution,
The expected value for Y is
Consider,
Take derivative with respect to q on both sides of the expression.
Again take derivative with respect to q on both sides of the expression.
The value of
Hence, the value of
The value of variance of Y is,
Hence, the variance of Y is
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Chapter 3 Solutions
Mathematical Statistics with Applications
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