Suppose two random subsets A and B of {1,2,....,n} are chosen independently, whe

Question

Suppose two random subsets A and B of {1,2,....,n} are chosen independently, where every subset of {1,2,....,n} is equally likely. Let the random variable X be (A union B).
a. calculate the probability mass function for x.
b. calculate E[X] using linearity of expectation.
Suppose two random subsets A and B of {1,2,....,n} are chosen independently, where every subset of {1,2,....,n} is equally likely. Let the random variable X be (A union B).
a. calculate the probability mass function for x.
b. calculate E[X] using linearity of expectation.

Explanation / Answer

a) 1/n

b) A + B

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