For a continuous random variable with the pdf function f(x) = 0.09375(4 - x^2) if 2 <= x <= 2, and 0 otherwise, solve the following: (a) Compute P(X > 0). (b) Compute P(−1 < X < 1). (Enter your answer to four decimal places.) (c) Compute P(X < −1.2 or X > 1.2). (Round your answer to four decimal places.)

Suppose that approximately 40% of the population has Type O+ blood. You take a sample of 5 persons. Let Y denote the number of persons in the sample with Type O+ blood. Find each of the following.  (a) Pr{Y = 2} =  (b) Pr{Y < 2} =  (c) Pr{Y ≥ 2} =

Given the pdf: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance of X using the pdf. (ii) Find the moment generating function of X. (iii) Find the mean and variance of X using the moment generating function.

The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).