B1. Let X be a continuous random variable with PDF 2 f(x) = ½ ½ (2 - x) 9 and f(x) = 0 otherwise. for 1x c (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X

Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.

Q6

If the pdf of a random variable X is f(x) = { 0.15-0.15(x-0.5), x ≥ 0.5 otherwise Find the moment generating function and use it to find the mean and variance of X.

Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)

C1. Let X be a continuous random variable with PDF f(x) = ? (2 – a) for –1 1)? (c) Calculate the expectation and variance of X. (d) Let Y (X2 – 1). What is the expectation of Y?

If E[X] = 1 and Var(X) = 5, use definition of variance and properties of expectation to find (a) E[(2 + X)^2] (b) V ar(aX) for any constant a. (c) V ar(X + b) for any constant b. (d) V ar(4 + 3X)

The density function of X is -120x- 0, f(x) = (2(x - 1), (a) Find the mean E(4X+3); (b) Find the variance 3x+2. 1 < x < 2, elsewhere.

3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?