Concept explainers
Suppose that Y is a binomial random variable with n > 2 trials and success probability p. Use the technique presented in Theorem 3.7 and the fact that E{Y(Y − 1)(Y − 2)} = E(Y3) − 3E(Y2) + 2E(Y) to derive E(Y3).
Derive
Explanation of Solution
Calculation:
Theorem 3.7:
If Y is a binomial random variable based on n trials and success probability p, then
The random variable Y is binomial random variable having
Consider the term
Add and subtract 3 to the term
Suppose that
It is obvious that,
That is,
The value of
Hence, the expression is
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Chapter 3 Solutions
EBK MATHEMATICAL STATISTICS WITH APPLIC
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