Question

Consider an random variable A generated from two independent, non-identically distributed rvs, B and C:

B ~Ber(

$C \sim \textup{Bin}(n,p)$

Here we would say that A has a zero-inflated binomial distribution, which is like a binomial but with a spike at zero. This is a type of mixture, since any given realization of A can be viewed as having come from one of a number of distinct distributions, in this case either a zero-only distribution or a binomial.

Write out an expression for the probabilty P(A = 0) in terms of probabilities of B = 0, B = 1 and C = 0. [Hint: think about what outcomes or combinations of outcomes of C and B must occur for A = 0.]

Answer 1

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