A game works as follows- You have to pick 4 integers (without replacem.pdf

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A game works as follows: You have to pick 4 integers (without replacement) between 1 and 14 (inclusive). The game operator chooses 4 numbers (without replacement) between 1 and 14 (also inclusive). If exactly two of the numbers youtinave chosen are among the four chosen by the operator, you win $10 ; if exactly three of the numbers you have chosen are among the four chosen, you win $100 ; if all four of your numbers match you win $1000 . Otherwise, you have to pay $75 . A random variable X represents your profit. (a) Complete the probability distribution of X , your profit resulting from playing this game, listing from smallest to largest. For each probability, round to at least four decimals in your answer. (b) Sketch the distribution of probabilities from (a), with the values of X on the x -axis and P ( X = x ) on the y -axis. What can you say about the tendency of the random variable X ? The distribution of X is (c) Compute the expected value of X and the standard deviation of X . E ( X ) = (round to two decimals in your answer) S D ( X ) = (round to two decimals in your answer).

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