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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Do number 11
Please write

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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