# Question

From a set of n elements, a nonempty subset is chosen at random in the sense that all of the nonempty subsets are equally likely to be selected. Let X denote the number of elements in the chosen subset. Using the identities given in Theoretical Exercise 12 of Chapter 1, show that

Show also that, for n large,

Var(X) ~ n/4

in the sense that the ratio Var(X) to n/4 approaches 1 as n approaches ∞. Compare this formula with the limiting form of Var(Y) when

P{Y = i} = 1/n, i = 1, . . . , n.

Show also that, for n large,

Var(X) ~ n/4

in the sense that the ratio Var(X) to n/4 approaches 1 as n approaches ∞. Compare this formula with the limiting form of Var(Y) when

P{Y = i} = 1/n, i = 1, . . . , n.

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