iid 2. Let Y1,..., Yn-1 xỉ and consider U = E Y;. n-1 i=1 (a) Show that U~ (b) What is the expectation of U? (c) If o? is a constant, what is the expectation of U? n-1

1. What is the expectation of the function g(x1, x2) = x, using the following joint PMF? X1 3 6 2 35% 15% 4 20% 30%

Which of the following statements regarding probabil ity is always correct? A A probability can range from 0 to 1. A probability close to 0 means the event is not likely to happen. A probability close to 1 means the event is like C ly to happen All the above are true. D

Q1 Let X1 and X2 be independent exponential random variables with identical parameter A. Q1(i.) Find the distribution of Z = max(X1, X2). Q1 (ii.) Find the distribution of Y = min(X1, X2). Q1(iii.) Calculate E[Y]. Q1(iv.) Calculate E[Z]. Q1(v.) Using the relation Z = X1+X2 – Y, Calculate E[Z] and verify that it agrees with the calculation done in part (iv.)