Suppose the probability of a sh's roe hatching into N = 11 baby sh is given by the Poisson distribution with parameter 2L (let T = 1), and assume the probability of a baby sh surviving to develop into an adult sh is p. Also assume the sh are independent as far as survival is concerned. The number of sh that survive is denoted by the random variable K. (You could use your computer to assist you if needed.) (a) What is the conditional probability of having k adult sh surviving given n baby sh were hatched, i.e. P(K = kIN = n)? (3pts) (b) Write down an expression for the probability of having total k survivors P(K = k) (your answer should be an innite series). (3191's) (c) Find the probability of having no survivor if p = 0.05 and A = 100. (4pt)