Identify binomial model and compute moments

Q: Identify binomial model and compute moments

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Question

Tossing N Balls Into a Cup (Independent Hits with Probability p)

You toss N independent balls toward a cup. Each ball lands in the cup with probability p, where 0 < p < 1. Let K be the number of balls that land in the cup.

Answer the following:

(a) What is the distribution of K?

(b) Write its probability mass function (pmf) P(K = k).

(c) Compute E[K] and Var(K).

(d) Briefly state how your answers would change if the tosses were dependent or if the success probability varied by ball.

Identify binomial model and compute moments

Tossing N Balls Into a Cup (Independent Hits with Probability p)

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