Question 2 (total 20 marks) When a fair coin is tossed, 10 points are scored if a head is obtained and 20 points are scored if a tail is obtained. Suppose that the coin is tossed two times and let the random variable X be the total score obtained. (a) What is the state space of X? (b) What is the probability mass function of X? Draw the line graph of the probability mass function. (c) What is the cumulative distribution function of X? Draw the graph of the cumulative distribution function. (d) What is the expectation of X? (e) What is the standard deviation of X?

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