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ACTL1101 Final Exam
1. Problem
Let X and Y be two independent Geometric(p) random variables with the same parameter
(0 < p < 1). Which of the following statement(s) is(are) necessarily TRUE (select all that
applies)?
(a) X + Y is a Geometric random variable
(b) minimum(X,Y ) is a Geometric random variable
(c) maximum(X,Y ) is a Binomial random variable
(d) X + Y is a Negative Binomial random variable
(e) minimum(X,Y ) is a Binomial random variable
Solution
(a) False
(b) True
(c) False
(d) True
(e) False
2. Problem
Among all Americans voters, 6% are Asian-American, 48% voted for Trump, and 2.2% are
both Asian-American and voted for Trump. If you pick an American voter at random, what
is the probability they are neither Asian-American, nor voted for Trump? [The choices are
expressed in decimal values, i.e. 0.05 ≡ 5%.]
(a) 0.54
(b) 0.59
(c) 0.65
(d) 0.48
(e) 0.73
Solution
Denoting the event ‘A: Asian’ and ‘T : Trump’. We seek
Pr[(A ∪B)C ] = 1? Pr[A ∪B] = 1? (0.48 + 0.06? 0.022) ≈ 0.482.
(a) False
(b) False
(c) False
(d) True
(e) False