Identify binomial model and compute moments

Q: Identify binomial model and compute moments

This question evaluates understanding of probability distributions and independence by identifying the binomial model and computing its probability mass function, expectation, and variance, assessing core probabilistic competency for data scientist roles.

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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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Identify binomial model and compute moments

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

Solution

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