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A random variable can assume the values 0, 1, 2,..., n, and its corresponding frequencies are proportional to the coefficients nC0, nC1, nC2,..., nCn. What is the variance of this distribution?

1. n/4
2. n/3
3. 2n/5
4. None of these

Correct answer: n/4

Solution

Frequencies proportional to nC0,nC1,...,nCn give a binomial distribution with p=1/2. Variance = n·p·(1-p) = n·(1/2)·(1/2) = n/4.

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