Quiz #2
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| |
answer |
| 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.)