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of the binomial distribution. EXERCISE 3 Answer the following questions: a. Let X1, X2, X: be i.i.d. random variables N(0, 1). Show that Y, = X, + 8X, and Yz = X2 + 6X, have bivariate normal distribution. Find the value of 6 so that the correlation coefficient between Y1 and Yo is p = ;. b. Let X and Y follow the bivariate normal distribution with parameters #1, #2, 01, 02, p. Show that W = X - 1 and Q = (Y -#2) - p" (X - 1) are independent normal random variables.2. A continuous random variable X has the probability density function fx (t ) = at the' 0 5), and (iii) P(X = 3)