Exam P Practice Question 929

Study guide: Exam P-1

A random sample of size 3 is drawn without replacement from the integers $\{1, 2, \ldots, n\}$ . The maximum value in the sample is denoted $M$ .

The probability function of $M$ is $P[M=m] = \dfrac{3(m-1)(m-2)}{n(n-1)(n-2)}$ for $m=3,\ldots,n$ .

Calculate $\text{Var}(M)$ .

A) $\dfrac{3(n+1)(n-3)}{20}$
B) $\dfrac{3(n-1)(n-3)}{80}$
C) $\dfrac{3(n+1)(n-3)}{80}$
D) $\dfrac{(n+1)(n-1)}{20}$
E) $\dfrac{(n-1)(n-3)}{20}$

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