5. You nd an unfair six-sided die. The probabilities of rolling each of the numbers 1 through 5 are identical and given by p. The expected value of a single roll is exactly 5. a.) What is the probability of rolling a 6? Note: Your answer must not be in terms ofp. b.) What is the variance in the value of a die roll? Reminder: If you did not solve part (a), your answer may be in terms ofp and the solution to part a. 6. Use a combinatorial proof to prove the following identity: 52-3-48-3-44-3 _ (13) , (4)3 3!(2!)3 _ 3 2 Make sure to include the following parts: . Story for what you are counting . Explain how the left-hand side counts what you wanted . Explain how the right-hand side counts what you wanted . Conclude that the identity holds Hint: One possible story for this question would use hands of cards. A standard deck contains 52 cards. Each card has one of 13 ranks and one of 4 suits