4. For each statement below, determine whether the statement is true or false. Circle your answer if you are writing your solutions on this document. If you are writing your solutions in a separate document, write TRUE or FALSE for each statement. (a) TRUE FALSE Suppose X1, X2, . . . ,Xn is a random sample of n. _observations from a normal distribution with mean p. and variance 02. The T = Sj'fT'ET/ follows a Student's 33 distribution with n degrees of freedom (note: X is the sample mean and S is the sample standard deviation). (3 pts) (b) TRUE FALSE Consider two events A and B such that P(A) = 0.3, P(B) = 0.2, and P(A D B) = 0.06. Then A and B are mutually exclusive. (3 pts) (c) TRUE FALSE Suppose X is a continuous random variable with pdf f (3:) Then P(X = as) can take any value between 0 and 1. (3 pts) ((1) TRUE FALSE If Y is a random variable with pdf y) = 116y28w/2 for y > 0 (0 otherwise], then Y is a Chi-squared random variable with 6 degrees of freedom. (3 pts) (e) TRUE FALSE If X and Y are independent random variables with standard deviations ox = 3 and cry = 4, respectively, then the standard deviation of W = X +Y is given by JW = 7. (3 pts)