2. consider the experiment of rolling exactly 3 fair dice independently. let x1, x, and x3 denote the values that the first die, the second die and the third die roll respectively. (a) what is the size of the sample space of this experiment? (b) let max - max{x1, x2, x3} represent the variable that measures the maximum value that shows up among the three dice. what is the range of max? (c) what is the probability distribution of the random variable mar? (d) calculate the value of e(max) using the probability distribution of max from your answer to the previous question (e) let sum x1 + x2 + x3. what is the range of the random variable sum? (1) calculate the value of e(sum). (hint: do you need to know the probability distribution of sum in order to calculate e(