Let z be a bernoulli random variable with parameter p and w an independent binomial random variable with parameters n and p. What is the distribution of z + w?

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Mathematics

Maximo Haley

12 June, 17:28

Let z be a bernoulli random variable with parameter p and w an independent binomial random variable with parameters n and p. What is the distribution of z + w?

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Barrett Rosales · Answer 1

It is known that if Z is a binomial random variable with parameters n and p and in addition, W is a binomial random variable, independent of X, with parameters m and p, it is assumed that the variable R = Z + W, is a binomial random variable with parameters (n + m and p. In this case, m = 1. Therefore, R is a binomial random variable with parameters (n + 1) and p.