Exercise 1

Suppose X is a standard normal random variable. Consider the random variable Y = X4. (a) Find P(Y > 10). (b) Give the probability density function of Y.Suppose Z 1, Z2, . . . , Z25 are independent uniform random variables on the inter- val [2, 7]. (a) Suppose Z is the average of 21,22,. . . 225. Approximate the probability that Z is less than 4.3 using normal approximation. (b) Let M be the minimum of 21,22, . . . , Z25. Find the probability that M is less than 2.2, rounded to nearest .XXXX