Question: a) If X Pois() and g is any function, show that : E Xg(X)] = E [g(X + 1)] (This is called the Stein-Chen identity

a) If X Pois() and g is any function, show that :

E Xg(X)] = E [g(X + 1)]

(This is called the Stein-Chen identity for the Poisson.)

(b) Find the third moment E [X3] for X Pois() by using the identity from (a) and the fact that X has mean and variance . Simplify your answer.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
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 Mathematics Questions!

Q:

A television signal (video and audio) has a bandwidth of 4.5 MHz. This signal is sampled, quantized, and binary coded to obtain a Pulse code modulation (PCM) signal. a) Determine the sampling rate if...

Q:

HHelp. me to solve the following attached questions. 4 Labor market equilibrium with proportional taxation Consider a model in which a household derives utility from consumption c and leisure 1...

Q:

Please answer all the required questions in detail I hope the answer is not copy-paste I hope that the answer will be according to the concepts in the chapter 3 The following article summarizes the...

Q:

Problem 6: Which of the following represents a function of x? Write Yes or No. (1 pt each) Problem 7: Determine the domain for each of the following. Write your answer using interval notation. (a, e,...

Q:

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Q:

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...

Q:

MATH 107 Quiz 5 Name Click here to enter text. Each question is worth 5 points. Questions 1 - 5 are multiple choice; you do not need to show your work. Short answers for Questions 6 - 10; show your...

Q:

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Q:

SOLVE Questions 1-5: PLEASE AND THANK YOU 1: What is the difference between homogenous and non-homogenous differential equation? Write an example for each and solve it. 2: What is the main formula to...

Q:

All the information are in it (i) g(x) = x?(x + 5)%(x 1)(x 4) (a) Degree: ; Leading coefficient: ; based on this the end behavior is: (b) the x-intercepts: X-intercept Multiplicity Bounce or cross?...

Q:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

The Sport department at a school purchased gears for different sports: Football, Netball, and Athletics. A gear for a particular sport consist of three different components. The total expenditure...

Q:

Under current law, shareholders prefer dividends because salaries, interest, and rent are fully taxed while dividends receive preferential tax treatment.

Q:

2. A diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the upper left corner to the lower right corner. Formally, an nxn matrix A = [aij) is...