Consider some 4-sided dice. Roll two of these dice. Let X be the minimum of the two values that appear. Let Y denote the maximum. Let Aj be the event containing all outcomes in which the minimum of the two dice is j or greater. Let Xi indicate whether Aj occurs. Then X = X1 + X2 + X3 + X4.
a) Give the set of all outcomes when rolling the two 4-sided die.
b) Give the list of elements that are in each of Ai, A2, A3 and A4.
c) Find P(A for each j =1, 2, 3 and 4.e
d) Find the expected value of X by finding the expected value of the sum of the indicator variables.