Can anyone please answer the question in number 2. Thanks. A roulette wheel cons

Question

Can anyone please answer the question in number 2. Thanks.

A roulette wheel consists of 18 black slots, 18 red slots, and 2 green slots. If a gambler bets $10 on red, what is the gambler's expected gain or loss? Suppose an insurance company pays the amount of $1,000 for lost luggage on an airplane trip. From past experience, it is known that the company pays this amount in 1 out of 200 policies it sells. What premium should the company charge to break even on average? The number of light switch turn-ons at which the first failure occurs is a random variable X whose probability distribution is given by: f(X = n) = c, (9/10)^n - 1, n = 1, 2, ... (a) Determine the constant c (b) Calculate the probability that the first failure will not occur until the 10th turn-on. The number of particles emitted by a radioactive source in an hour has a Poisson distribution with parameter lambda = 20. Find the probability that exactly one particle is emitted in a period of 2 minutes. Suppose that a fair die is rolled 100 times. Let X_i be the value obtained on the i th roll. (a) What is P(sigma^100_i = 1 X_i = 100)? (b) What is P(signma^100_i = 1 X_i = 101)? (c) What is E[sigma^100_i = 1 X_i]? Give an example of two discrete random variables, X and Y, with the same set of possible values, such that Var (X + Y) notequalto Var(X) + Var(Y). Show all relevant computations.

Explanation / Answer

Expected premium = Expected payout for the insurance company to break even.

Premium = P(Loss) Payout(Loss) + P(No Loss) * Payout(No loss)

Premium = 1/200 * 1000 + 199/200*0 = 5

Hence, premium should be equal to 5 dollars for it to break even.

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