Please answer the question in number 1. Thanks. A roulette wheel consists of 18
ID: 3217502 • Letter: P
Question
Please answer the question in number 1. 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
A roulette wheel has 18 red slots and 20 others(18black+2 green)
Now P(ball goes into the red) = 18/38 and
P(Ball goes into black or green) = 20/38
Therefore the expected payoff = 10 * 18/38 + (-10) * 20/38 = (180-200)/38 = -20/38 = $-0.526
The gambler will lose $-0.526