Problem 4. Random Variable Ranges For all of these problems, you may assume the sample space S is nite. (a) Show that if A is a random variable whose range is [10, 10] (that is, A(w) is a real value between 10 and 10, inclusive, for each outcome w E S), then 10 3 Ex [A] g 10. (b) For any a: E [10, 10], give an example of a random variable A which takes real values between 10 and 10, inclusive, such that Ex [A] = 2:. (c) The previous two parts show that if A is a random variable whose range is [10, 10], the set of possible values of Ex [A] is exactly the set {10, 10]. Similarly, show that if A is a random variable whose range is [ 10, 10], then the set of possible values of Ex [A2] is exactly [0,100]