Q1. Andrew and Bertha each flip a coin a certain number of times in such a way that all possible sequences of Heads and/or Tails are equally likely. Andrew flips 2 times while Bertha flips 3 times. Let A denote the number of Heads in Andrew's 2 tosses and let B denote the number of Heads in Bertha's 3 tosses. Let X = min(A, B) and let Y = max(A, B). Then Var(X + Y) is closest to
(a) 5/2
(b) 3/8
(c) 5/8
(d) 3/2
(e) 5/4
Q2. Suppose that S is the sum of 6 random draws with replacement from the finite population
χ = {0, 0, 0, 2, 3, 4, 4, 4, 5, 6, 8, 15, 15, 20}.
Then E(S) is closest to
(a) 36.86
(b) 86
(c) 516
(d) 86/14
(e) (86 * 14)/6
Q3. Suppose that A is the average of 9 random draws with replacement from the finite population χ = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then Var(A) is closest to
(a) 77/18
(b) 2.75
(c) [(385/10) - (55/10)2]/9
(d) 0.82
(e) 33/4