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A casino roulette wheel has 18 red numbers, 18 black numbers and 2 green numbers. 1. We bet $5 on the black numbers. If a

A casino roulette wheel has 18 red numbers, 18 black numbers and 2 green numbers. 1. We bet $5 on the black numbers. If a black number is drawn the player wins $5, otherwise he loses his $5. Let X be the random variable indicating the player's net gain for the $5 bet. Give the distribution of X. 2. Calculate the expectation and standard deviation of the net gain X. 3. If we bet $50 (instead of $5), what are the expectation and the variance of the net gain? 4. Considering the bet of $50, what is the probability that the player will lose $50

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