Question: 3. (Cards, 10 points). You choose a random card from a standard deck of 52 cards and assign a value to it as follows: Ace

3. (Cards, 10 points). You choose a random card from a standard deck of 52 cards and assign a value to it as follows: Ace gets 1, number cards (2 to 10) get their number as the value, and face cards (Jack, Queen, King) get 11. Let X be a random variable that represents the value of the card chosen from the deck. Let Y = 2X and Z = X?. (a) Determine the range of X, its PDF and CDF. (b) Evaluate Pr(Y 2, (d) [X - Y)

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