Problem 2. Suppose I have 10 cards, labeled 1 through 10. They're completely shuffled so every permu- tation is equally likely. You draw 2 cards and give me the smaller card. Let X be the random variable that is my card's value. (a) What is the probability mass function (pmf) and cumulative distribution function (cdf) of my card's face value, X? We'll denote these p(x) and F(r) respectively. Plot the cdf. (b) What is the expected value of X? We'll denote this E[X].

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