Consider a binomial experiment with n = 10 and p = .10.a. Compute f(0).b. Compute f(2).c. Compute P(x ≤ 2).d. Compute P(x ≥ 1).e. Compute e(x).

2. Let X and Y be independent random variables with E[X] = 4, Var[X] = 84, E[Y] = 6, and Var[Y] = 54. Find E[5X + 2Y - 18] - b. Find E[-3Y+X+3] -a. -с. Find E[X2] d. Find ox e. Find E[Y2] f. Find Oy g. Find Var[X+3Y - 6] h. Find Var[3X - 2Y + 35] Find E[(2X - 8)/5] j. Find Var[(2X - 8)/5] i.

A random variable, X, has a pdf given by The expected value of Y is O a. 3/5 O b. 5/3 O c. 7/5 O A random variable Y, is related to X by Px(x) d. 7/3 = 1 -3 < x < 1. and 0 otherwise 4 Y = X²

1. Random variable X has p.d.f -6z 6e fx(z) otherwise and let Y = eX. Calculate E(X)

Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27

8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15

4. A particle moves on the x- axis starting at x = 0. With equal probability, the particle moves to the left or right one unit. Let X denote the position on the x- axis after four moves. (a) Find px(x). Notice that X can take on -4,-2,0, 2, 4. Fill out the table below. xPx(x) (b) What is the expected position of the particle after four moves. That is, compute E(X). Express your answer as a fraction in lowest terms.

Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?

2. Find E(X) and Var(X) if a. P(X = 0) = 0.2, P(X = 1) = 0.3, and P(X = 2) = 0.5. b. X is the number of successes in 200 Bernoulli trials each with probability of success 0.7.