3. An auditor is checking tax returns for irregularities. To make their boss happy, they need to nd K returns with irregularities to review in detail, and the auditor estimates that K ~ Poi(10). The probability that any return has an irregularity is independently 0.05. Let X = the total number of returns the auditor checks. (a) [1] What are the conditional distribution and conditional range of X |K = k? (b) [1] Find E[X|K = k] and Var(X|K = k). (c) [2] Write down E[X |K] and Var(X|K). Explain briey why these are random variables. (d) [2] Find E[X]