Imagine that instead of having a standard six (6

6)-sided die, you are playing a game with an eight (8

8)-sided die.

a) Part of this game involves rolling the8

8-sided die two times in a row and using the higher number that is rolled. What is the probability distribution function of the random variable that describes rolling an8

8-sided die twice and choosing the higher number?

b) What is the expected value and standard deviation of the probability distribution function of the random variable that describes rolling an8

8-sided die twice and choosing the higher value?

c) If you roll an8

8-sided die twice and choose the higher value, what is the probability that you get a number higher than5

5?

d) Now consider ann

n-sided die, labelled with the numbers1

1ton

n, each number having an equal probability of being rolled. If you roll this die twice and choose the higher number, what is the probability that you get a1

1ifn