(a) Write down the probability distribution of x. Solution: p(x = 0|μ) = 1− μ, so p(x|μ) = μx(1− μ)1−x, this is known as the Bernoulli distribution. (b) Show that this is a proper probability distribution, i.e. the probability sum up to 1. What is the expectation and variance of this distribution? Solution: ∑ x∈{0,1} p(x|μ) = p(x = 0|μ) + p(x = 1|μ) = 1− μ+ μ = 1 E(x) = ∑ x∈{0,1} xp(x|μ) = 0× p...
