If XXx be Bemoulli random variables, with parameter , then the sufficient statistic for is ПХ. a) ΣΧ b) e d)

4) Let x be a binomial random variable with n = 8, p = .6. Find: a) u = np b) o = bdu,

12

Exercise 12. Let X, Y, Z ~ N(0, 1) be independent. Determine the distribution, expectation and variance of the following random variables: a) X + Y + Z b) X² + y² + Z²

5. Let X and Y be independent random variables with each following N(0,1). Consider the random variable W defined by { if XY > 0, if XY 0 and W < 0. Show work.

What will be the expected value

Let Z be a standard normal variable. Find the value of z if z satisfies P(Z > z) = 0.6331. a) 00.35 b) O-0.3 с) О-034 d) 00.34 e) 00.30 D O None of the above. Question 29 Suppose X is a normal random variable with u = 35 and o = 10. Find P(21.4 < X < 39.7). a) 005586 b) 00.5337 c) O0.5939 d) O0.2323 e) 0 0.2478 f) O None of the above.

4.9Q) Let P and Q be two random variables such that E(P) =7 and E(Q)= 4, then E(4P+3Q+5) is: 1)42 2)44 3)45 4)38