Determine independent exponential distribution of parameter

Question

Assignment:

1. Consider K independent rvs y_k, k = 1, 2,...,K, with exponential distribution of parameter

λ. Let y_max = max_k{y_k} and y_min = mink{y_k}.

Find the PDF of y_max and y_min and determine whether they are exponentially distributed themselves.

2. Let y be an exponential rv of parameter λ. Consider another rv v that, conditioned on y = a, is Poisson distributed with parameter a. Find the PMD of v.