Imagine that instead of having a standard six (6)-sided die, you are playing a game with an eight (8)-sided die. a) Part of this game involves rolling the 8-sided die two times in a row and using the higher number that is rolled. What is the PDF of the random variable that describes rolling an 8-sided die twice and choosing the higher number? b) What are the expected value and standard deviation of the PDF of the random variable that describes rolling an 8-sided die twice and chooses the higher value? c) If you roll an 8-sided die twice and choose the higher value, what is the probability that you get a number higher than 5? d) Now consider an n-sided die, labeled with the numbers 1 to 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 a 1 if n ?