Question

Question 2 6 marks One day last November, a devastating storm over the Elephant Island, out of 2m penguins which formed mcouples, precisely k of them died. (Here, m,k EN and 0 Sk S 2m.) Assuming that these k decreased penguins were picked by Nature at random and with equal probabilities 2(a) Give the probability mass function for the number of surviving penguin couples. 2 (b) What is the expected value of the number of surviving couples? 2 (c) What is the variance of the number of surviving couples?

Answer 1

ost novem be a ievrta-ting stom mg Storm ich tor me proloabili mass fnc ion tor the umbc at Servivin pengwix couplsivenh and s prev te im Grn ampie -thxec sill be 2e

deacths k is 3 or more hun, be huw ben ol Possible ualua possible imocureuces xso, (m)* (mtりん

the a ent) (mm) 2-