We are tossing a coin and a 6 sided die. Let H and T represent Head up and tail up respectively from the coin flip, and the numbers 1,2,3,4,5,6 represent the rolls from the die. (For example, H3 represents the event of Heads up from the coin and rolling 3 from the die) (10 pts)

(a) Find the sample space of this experiment and find the sample size (number of elements in the sample space). (5 pts)

(b) Let x be the discrete random variable that assigns numbers same as the die roll to each events. For example, x assigns 2 to both H2 and T2. Use this randomvariable to find the expected die roll. (5 pts)

You only need to submit (1) parts (a) and (b)

The problems below are optional practice.

(c) Find the variance and standard deviation of x.