## Quiz #2

Answers are given in the answer boxes below. Scroll down for explantions for the answers (given in red).

Be sure to put your name on this quiz. Write the letters corresponding to the correct answers in the answer boxes below.

Question 1 C
Question 2 A

#### Question 1

W is a random variable with the following pmf:
pW(0) = 0.4, pW(1) = 0.5, pW(10) = 0.1.
What is the value of E(W)?
• [ A ] 1/3
• [ B ] 1
• [ C ] 1.5
• [ D ] 11/3
• [ E ] 5
• [ F ] 5.5
E(W) = 0*pW(0) + 1*pW(1) + 10*pW(10) = 0*0.4 + 1*0.5 + 10*0.1 = 1.5.

#### Question 2

Consider making a random selection from a population of animals of which 10% of them suffer from a particular illness. (Assume that each animal in the population has an equal chance of being chosen.) Let X be a random variable such that X is equal to 1 if the random selection results in an animal having that particular illness, and X is equal to 0 otherwise.

What is the expected value of X?
• [ A ] 0.1
• [ B ] 0.5
• [ C ] 0.9
• [ D ] 1.0
• [ E ] 10
E(X) = 0*pX(0) + 1*pX(1) = 0*0.9 + 1*0.1 = 0.1.
(One could also use the fact that X is a Bernoulli(p) random variable, with p (the probability of "success" (with, in this case, choosing an ill animal corresponding to a success)) equal to 0.1. Since for a Bernoulli random variable the expected value equals the probability of success, the desired expectation is equal to 0.1.)