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A discrete variable takes the values 0, 1, 2,..., n with frequencies proportional to the binomial coefficients C(n,0), C(n,1),..., C(n,n). Find the mean of this distribution.

1. n(n+1)/4
2. n/2
3. n(n-1)/2
4. n(n+1)/2

Correct answer: n/2

Solution

Frequencies proportional to C(n,i) give probabilities C(n,i)/2ⁿ, the Binomial(n, 1/2) distribution, whose mean is n/2.

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