Question 6: (from chapter 4) Tay-Sachs is a rare fatal genetic disease occuring chiefly in childeren. Suppose that we limit ourselves to families which have (a) exactly three children, and (b) which have both parents carrying the Tay-Sachs disease. For such parrents, each child has independent probability 1/4 (one out of four) of getting the disease. Write X to be the random variable representing the number of children that will have the disease. a. Show (without using any knowledge you might have about the binomial distribution!) that the probability distribution for X is as follows: k 0 2 3 P(X = k) 27/64 27/64 9/64 1/64 (b) Calculate the expected value and the variance for the variable X as defined above