申論題

(10%) Consider a Bernoulli random variable X with P(X = 1) = p and P(X = 0) = 1 - p, and a continuous random variable Y which is conditioned on X. The condi- tional probability distribution function of Y given X is defined as follows: fyix(y|1) is a Gaussian distribution with mean pu and variance σ², and  is an exponential distribution with mean 1/λ.