Do number 11Please write 11. Let Y be a random variable with density functionf(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 anddeviation 10 mm.(a) What is the probability that a randomly chosen bolt has a width betweenand 958 mm?(b) What is the appropriate value for C such that a randomly chosen bolthas a width less than C with probability 0.8531?13. Find P(|X - μ| ≤ 2o) for the exponential random variable. Compare withresponding probabilistic statements given by Tchebysheff's theorem and the errule.14. The weekly amount of downtime Y (in hours) for an industrial machine has a

"As per the Bartleby guidelines, we can solve only one question at a time.Therefore, we are solving…

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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 29CR

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Question

Do number 11 Please write

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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