Let Y be a continuous random variable having the standard beta distribution with parameters a = 3 and 38. That is, the pdf of Y is of the form Find the cdf F of Y. f(y) r(11) (3x² (1-x)7 r(3)r(8) { if0 ≤ y ≤ 1 otherwise.

f (x) = 4xc for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is apdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphsof the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.

The amount of time necessary for assembly. line workers to complete a product is a normal distribution with a mean of 18 minutes and a standarddeviation of 3.5 minutes. a )Find the probability that a product is assembled in less than 22 minutes. b)What is the cut-off time (X) for the top 12% of workers?

Let X₁, X2, X3, be a random sample from a discrete distribution with probability function p(x) = for x = 0, for x = 1, otherwise. Determine the moment generating function M(t) of Y = X₁X₂X3- A. exp(t) B. (exp(t)+7)/8 C. (exp(1/2)+1)/3 D. (exp(t)+63)/64 E. (exp(t)+1)/4