Let x be a random variable distributed as Bernoulli with parameter p ∈ (0, 1), x ∼ ber(p). That is, with p.m.f. px(x = n) = (1 − p)^(n) * p^(1−n), n = 0, 1. Compute the p.m.f.’s of the following random variables:
A) Binomial distribution with parameters n and p
B) Geometric distribution with parameter p
C) Poisson distribution with parameter λ = -log(1 - p)
D) Normal distribution with mean μ = p and variance σ² = p(1 - p)