Question: Suppose that given u, Y is Poisson with E(Y | u) = u , where may depend on predictors. Suppose that u is a

Suppose that given u, Y is Poisson with E(Y | u) = u µ, where µ may depend on predictors. Suppose that u is a positive random variable with E(u) = 1 and var(u) = τ. Show that E(Y) = µ and var(Y) = µ + τ µ². Explain how negative binomial GLMs and Poisson GLMMs with log link can follow as special cases.

Step by Step Solution

★★★★★

3.42 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose that given x Y is Poisson with EY u u Suppose that the conditional distribution of Y given u ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Categorical Data Analysis Questions!

Suppose that the number of customers arriving each hour at the only checkout counter in a local pharmacy is approximately Poisson distributed with an expected arrival rate of 20 customers per hour....

Suppose that Xi, i = 1, 2, 3 are independent Poisson random variables with respective means i, i = 1, 2, 3. Let X = X1 + X2 and Y = X2 + X3. The random vector X, Y is said to have a bivariate Poisson...

Suppose that the number of events occurring in a given time period is a Poisson random variable with parameter . If each event is classified as a type i event with probability pi, i = 1, . . . , n, ...

Given u, y is Poisson with E(y u) = u????, where u is a positive random variable with E(u) = 1 and var(u) = ????. Show that E(y) = ???? and var(y) = ???? + ????????2. Explain how you can formulate...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Student Major 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 A M M A M M E M O A E E M A O E M A M A M A O A M E E M A M Hotel Location Cost/Night Boulders Resort &...

BA 1605: Midterm Recap (Due: Feb. 27, 2015) Name _____________________________ 50 Student ID _____________________________ Section 01B 10:00~11:20 am Section 02B 01:00~02:20 pm [Questions 4 ~ 7] The...

v. Electrons are accelerated to 728V and are reflected from a crystal. The first maximum reflection occurs when glancing angle 8. Determine interplanar spacing of crystal vi. Evaluate compressibility...

A sphere of radius R carries charge density proportional to the square of the distance from the center: p= Ar2, where A is a positive constant. At a distance of R/2 from the center, the magnitude of...

Based on your calculations and understanding of semiannual coupon bonds, complete the following statement: Assuming that interest rates remain constant, the T - note s price is expected to .

5. In exercise 1, assume that the reward on arrival to the goal state is normal distributed with mean 100 and variance 40. Assume also that the actions are also stochastic in that when the robot...

In Exercise 15.8, the telephone holding times for Muzak and classical music were Muzak 0, 1, 4, 6, 3 Classical 13, 9, 8, 15, 7 a. For comparing these two groups with the Wilcoxon test, report the...

Refer to the previous exercise. For the actual experiment, suppose the participants using the tanning studio got ranks 1 and 2 and the participants using the tanning lotion got ranks 3 and 4. a. Find...

The nonparametric statistics textbook by Hollander and Wolfe (1999) discussed a study on a social skills training program for alcoholics. A sample of male alcoholics was randomly split into two...

which of the following queries is used tot determine how many customers belong to the Rochester city from the Customer table

Weasleys Wizard Wheezes produces and sells an assortment of practical joke items, had the following results for May. The budgets for June and July are also given. May (actual_ June (budget) July...

1. Which of the following is not a factor used in determining assessed value? a. Original price b. Improvements c. True cash value d. a, b and c are all factors used 2. Which of the following...