Question: 3. (7 points) *Let X be a Bernoulli random variable with probability of success p. Use the formula Var(X) = E(X2)-u to show that

3. (7 points) *Let X be a Bernoulli random variable with probability of success p. Use the formula Var(X) = E(X2)-u to show that Var(X) = p(1 - p). 4. (9 points) Kush has a friend who attends a nearby school, and they make a bet about the next basketball game between UNC and Duke. If UNC wins, Kush gets $20. If UNC loses, Kush pays his friend $30. Kush believes that UNC has a 70 percent chance of winning the game. 4.1. Let X be an indicator of whether UNC wins the game. What kind of distribution does X have? (a) Bernoulli (b) Geometric (c) Binomial (d) We do not have a name for this distribtion. 4.2. Let Y be the amount of money that Kush wins or loses from the bet. What kind of distribution does Y have? (a) Bernoulli (b) Geometric (c) Binomial (d) We do not have a name for this distribution. 4.3. What does Kush think is the expected value of his bet? (a) $14 (b) $5 (c) $0 (d) -$10

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