Suppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is Pg. Show that the mean of the posterior distribution of e will be a weighted average having the form YnX,+ (1 – Yn)Ho, and show that yn - 1 as n→ *.

Suppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is Pg. Show that the mean of the posterior distribution of e will be a weighted average having the form YnX,+ (1 – Yn)Ho, and show that yn - 1 as n→ *.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

See similar textbooks

Similar questions

Let X1, X2, ..., X10 be a random sample from a gamma distribution with α = 3 and β = 1/θ. Suppose we believe that theta follows a gamma-distribution with α = 28 and β = 17 and suppose we have a trial (X1 , ... , Xn ) with an observed x̄ = 28.2 What is the posterior distribution of θ What is the Bayes point estimate of θ associated with the square-error loss function?
A company has 9000 arrivals of Internet traffic over a period of 18,050 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= (μ^x • e^−μ) / x! to find the probability of exactly 2 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
A company has 8000 arrivals of Internet traffic over a period of 17,460 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= μx•e−μ x! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
A company has 9000 arrivals of Internet traffic over a period of 20,740 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)=μx•e−μx! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4 explain.