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11. Let Y be a random variable with density function cye-2y if 0≤ y <∞, elsewhere. 0 f(y) = {cu (a) Find the value of c which will make f(y) a valid density function. (b) Find the moment generating function of Y. (c) Find the mean and variance of Y.

11. Let Y be a random variable with density function cye-2y if 0≤ y <∞, elsewhere. 0 f(y) = {cu (a) Find the value of c which will make f(y) a valid density function. (b) Find the moment generating function of Y. (c) Find the mean and variance of Y.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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11. Let Y be a random variable with density function f(y) = { cye-2y if 0≤ y <∞, elsewhere. 0 (a) Find the value of c which will make f(y) a valid density function. (b) Find the moment generating function of Y. (c) Find the mean and variance of Y. 12. The width of bolts of fabric is normally distributed with mean 950 mm and deviation 10 mm. (a) What is the probability that a randomly chosen bolt has a width between and 958 mm? (b) What is the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8531? 13. Find P(|X - μ| ≤ 2o) for the exponential random variable. Compare with responding probabilistic statements given by Tchebysheff's theorem and the er rule. 14. The weekly amount of downtime Y (in hours) for an industrial machine has a
Transcribed Image Text:11. Let Y be a random variable with density function f(y) = { cye-2y if 0≤ y <∞, elsewhere. 0 (a) Find the value of c which will make f(y) a valid density function. (b) Find the moment generating function of Y. (c) Find the mean and variance of Y. 12. The width of bolts of fabric is normally distributed with mean 950 mm and deviation 10 mm. (a) What is the probability that a randomly chosen bolt has a width between and 958 mm? (b) What is the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8531? 13. Find P(|X - μ| ≤ 2o) for the exponential random variable. Compare with responding probabilistic statements given by Tchebysheff's theorem and the er rule. 14. The weekly amount of downtime Y (in hours) for an industrial machine has a
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