The square of a binomial count

Topic: Functions of random variables and limit theorems · more questions on this topic
The square of a uniform variable ›

Let X\sim\operatorname{Bin}(4,1/2) and Y=X^2. Give the probability mass function of Y.

Worked answer (click to show)

Y takes the values 0,1,4,9,16, and \mathbb{P}(Y=k^2)=\mathbb{P}(X=k)=\binom{4}{k}/16 for k=0,1,2,3,4.