Purchase Solution

Moment generating function and poisson distribution

Not what you're looking for?

Ask Custom Question

** Please see the attached file for the complete solution **
Shirley runs a real estate company. She counts the total number of flats that she sells everyday. Let X_t be the total number of flats she sells on day t (t=1,2,...,7), and let X be the total number of flats she sells for the week. Suppose X_t are independent and identically distributed Poisson distribution with expectation theta.

(Please see the attached file)
(a) Find the moment generating functions for X_1 and X

(b) Show X has a Poisson distribution with mean 7*theta

Attachments
Purchase this Solution
Solution Summary

This solution provides a step-by-step calculation of the moment generating function, and illustrates how to use the moment generating function to determine the probability distribution.

Solution Preview

Please refer to the pdf attached.

a) Let us recall the definition for the moment generating function for a random variable
(please see the attached file) With this in mind, let us find the moment generating function for X_1 first. By definition, since X_1 can only take values from 0, 1, ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Analyzing Poisson Distribution

    75257 Analyzing Poisson Distribution I would be grateful for an explanation to the following problem. Given that X possesses a Poisson distribution with mean u, show that the moment generating function of X is given by M(z)=exp(ue^z - u).

  • Probability and conditional distributions

    Given X~ Poisson ( ) and Y|X=x ~ Bin(x,p) Hence the Moment generating function of X, denoted by , is given by and Since Y|X=x follows a binomial distribution its moment generating function can be written as Now, =

  • Find the moment generating function for a Poisson random variable.

    170472 Find the moment generating function for a Poisson random variable. 3.86 ==== Show that the moment-generating function for the Poisson random variable with mean λ is given by M(t)= e^ ( λ( e^(t) -1) ) Ans: I started (seen below)

  • Probability and Cumulative Distribution Function

    b) Find the moment generating function of X, or Mx(t) c) Using your result in (b), find the E(X^2) 2.

  • Probability

    (a) What is the distribution of each ? Since the moment function of is , we can get the mean and , so the variance . (b) Compute the moment generating function of and identify the distribution of . Solution.

  • Probability

    107978 Moment generating functions and limit theorems Problems on moment generating functions --------------------------------------- 1. Let X and Y be independent normal rv's, each with mean mu and variance sigma^2.

  • Moment Generating Functions

    59782 Moment Generating Functions Can you please explain me how I can use the moment generating functions to find the limiting distribution: Suppose that Zi for N(0,1) and that Z1, Z2,...are independent.

  • Moment Generating Function of X

    The moment-generating function generates the moments of the probability distribution and thus uniquely defines the distribution of the random variable.

  • Probability: Moment Generating Functions and Poisson Process

    9351 Probability: Moment Generating Functions and Poisson Process 1.) Let X be a discrete random variable with probability mass function Pr {X=k} = c(1+ k^2) for k= -2, -1, 0, 1, 2. a) Determine c.

View More Related Solutions