Suppose you play a game in which you roll one die, and the payoff is the number of dots showing. What is the variance of this game?

Answer 1

Hello Janet,

Make a payoff probability table. It would start as:

payoff probability

$1 1/6

$2 1/6

...

and continue until you have listed all the possible results.

Then compute the expected value (mean) by multiplying each outcome times its probability and adding them up.

expected value = $1(1/6) + $2(1/6) + ...

To calculate the Variance:

1. square each value and multiply by its probability.
2. sum them up and we get Σx²p.
3. then subtract the square of the Expected Value μ