Please answer the question in number 6. Thank you for your help. A roulette whee
ID: 3217513 • Letter: P
Question
Please answer the question in number 6. Thank you for your help.
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 middot (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, be the value obtained on the ith roll. (a) What is P (sigma^100_i = 1 X_i = 100)? (b) what is P (sigma^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
6)
let the possible values are {0,1}
P(X=0) = 0.5, P(X=1) = 0.5
P(Y=0) = 0.4 , P(Y=1) = 0.6
possible values of X+Y are 0,1,2
P(X+Y = 0) = (0.5)(0.4) = 0.2
P(X+Y = 1) = (0.5)(0.6)+(0.5)(0.4) = 0.5
P(X+Y = 2) = 0.5*0.6 = 0.3
E(X+Y) = 0*0.2+1*0.5+2*0.3 = 1.1
Var(X+Y) = 0.2*(0-1.1)2 +0.5*(1-1.1)2 +0.3*(2-1.1)2 = 0.49
E(X) = 0*0.5+1*0.5 = 0.5 . , V(X) = 0.5*(0-0.5)2+0.5*(1-0.5)2 = 0.5
E(Y) = 0*0.4+1*0.6 = 0.6 . , V(X) = 0.4*(0-0.6)2+0.6*(1-0.6)2 = 0.24
V(X+Y) not equal to V(X) +V(Y)