(4) Consider the following table: x -2 0 4 6 8 p(x) .42 ? 0.18 0.14 0.1

(a) What would you replace the question mark in the table with to make it a probability distribution?

(b) Give two numbers that you could replace the question mark with that would guarantee that this table would not be a probability distributionfor different reasons. Identify the reason for each of those numbers.

c) Calculate the expected value for the probability distribution you obtained in (a).

(d) Your probability professor wants to replace the value 4 in the probability distribution in (a) to make a game based on it fair but keep all other values the same. What should she change the 4 to?

(4) (21 points) Consider the following table: a -2 0 4 6 8 10(53) .42 ? 0.18 0.14 0.1 (a) (3 points) What would you replace the question mark in the table with to make it a probability distribution? (b) (6 points) Give two numbers that you could replace the question mark with that would guarantee that this table would not be a probability distributionfor different reasons. Identify the reason for each of those numbers. (c) (6 points) Calculate the expected value for the probability distribution you obtained in (a). (d) (6 points) Your probability professor wants to replace the value 4 in the probability distribution in (a) to make a game based on it fair but keep all other values the same. What should she change the 4 to