Question 2: Three balanced coins are tossed independently. One of the variables of interest is X, the number of heads. Let Y denote the amount of money won on a side bet in the following manner. If the first head occurs on the first toss, you win $1. If the first head occurs on toss 2 or on toss 3 you win $2 or $3, respectively. If no heads appear, you lose $1 (that is, win -$1). X =0 X =1 X =2 X = 3 totals Y= -1 Y = 1 Y = 2 Y = 3 totals Please use at least five digits after the decimal point if rounding. a. Find E[XY]? [1 mark] Answer b. Are X and Y independent variables, explain how you know? [1 mark]