5.5.1 The probability distribution of a random variable D is the density curve of a uniform distribution at right. a. Determine the height that makes this a valid density curve. b. Find P(.3

12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))

9. Find the probability of z occurring in the indicated region. J 0 1.75

The discrete random variable Xhas the probability distribution given by: 7 9. 12 13 15 P(X=x) u/2 0.05 0.35 0.15 u d. Find the expectation of the random variable Y, whereY = X-4 Answer in exact fraction, or rounded to at least 4 decimal places.