Suppose a fair, two-sided coin is flipped. If it comes up heads you receive $5; if it comes up tails you lose $1. The variance of this lottery is what?
A)4.5
B)9.0
C)13.5
D)18.0

Question

Quizplus · Accepted Answer

The probability of getting heads is 0.5 and tails is 0.5. The expected value of this lottery is:

EV = 0.5($5) + 0.5(-$1) = $2

To find the variance, we need to find the squared difference between each possible outcome and the expected value, weighted by their respective probabilities:

Var = 0.5($5 - $2)^2 + 0.5(-$1 - $2)^2 = $9

Therefore, the variance of this lottery is 9.0. The expected value (EV) of this lottery is:
EV = (0.5 x 5) + (0.5 x -1) = 2

To find the variance, we first need to find the probability of each outcome:
- Probability of winning $5 = 0.5
- Probability of losing $1 = 0.5

The variance formula is:
Variance = (Probability of Outcome 1 x (Outcome 1 - EV)^2) + (Probability of Outcome 2 x (Outcome 2 - EV)^2)

Plugging in the values:
Variance = (0.5 x (5 - 2)^2) + (0.5 x (-1 - 2)^2) = 9.0

Therefore, the variance of this lottery is 9.0, which is answer choice B.

Suppose a Fair, Two-Sided Coin Is Flipped