The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.
The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The probability density function of a distribution is given by
x
f(x) = exp(-7).
Use differentiation to show that the probability density function has a maximum at x = 0.
The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1],
q = 1 - p and n is a positive integer. Use the moment generating function to find the
mean and variance of the distribution in terms of p, q and n.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F888bf1df-8bfe-4d18-9a90-5689a09de61e%2Ff3d63a75-2c8d-45ae-9026-8a8553da20e2%2Fd678w5_processed.png&w=3840&q=75)
Transcribed Image Text:The probability density function of a distribution is given by
x
f(x) = exp(-7).
Use differentiation to show that the probability density function has a maximum at x = 0.
The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1],
q = 1 - p and n is a positive integer. Use the moment generating function to find the
mean and variance of the distribution in terms of p, q and n.
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