Purchase Solution

Statistics: Moment Generating Function

Not what you're looking for?

Ask Custom Question

It is attached it is to show that if all Xi are normally distributed then

Y=a1X1+a2X2+...+anXn

Also is normally distributed

But please see the attachment as the question is a bit more specific than that as well. Thanks

File is uploaded in pdf and word

Attachments
Purchase this Solution
Solution Summary

Prove, using MGM, that a sum of independent normally distributed variables is also normal.

Solution Preview

We will use the following properties:
Lemma 1
If , then =
Lemma 2
If X and Y are independent, then
...

Solution provided by:
Chris Busu, PhD (IP)
Education
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
Recent Feedback
  • "Thank you "
  • "Thank You Chris this draft really helped me understand correlation."
  • "Thanks for the prompt return. Going into the last meeting tonight before submission. "
  • "Thank you for your promptness and great work. This will serve as a great guideline to assist with the completion of our project."
  • "Thanks for the product. It is an excellent guideline for the group. "
Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

View More Free Quizzes
Related BrainMass Solutions

  • Moment Generating Function of X

    In probability theory and statistics, the moment-generating function of a random variable X is wherever this expectation exists.

  • Mean Data

    33514 Moment generating function and Poissan's Dist. D.) Suppose X1 and X2 are independent exp. random variables, each with mean data and y=X1 and X2. What is the moment generating function for the random variable y?

  • Moment Generating Functions

    Now we want to get the moment generating function of U= , namely, we need to compute the expectation of . Note that the moment generating function for each Zi is Now, we are going to compute .

  • Moment generating function and poisson distribution

    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.

  • moment generating function and expected value

    170475 Finding E(Y) for a moment-generating function. 3.88 ===== Use your answer from 3.87 to show that E(Y) = aE(X) +b 3.87: [ If X is a random variable with moment-generating function M(t), and Y is a function of X given by Y=aX+b, show

  • Exponential Distribution

    To be done using summation or another method (Do not use the moment generating function (M.G.F)). Let X be an Exponential random variable with probability density function Now, (using the Gamma integral) , since =1!

  • Moment-Generating Function

    100576 Moment-Generating Function 1. Find the moment-generating function of X, where X is a triangular distribution, that is, the pdf of X is f(x) = (1 - |x|)*(I_(-1,1))*(x). 2. Show that b = E(X) minimizes E(X-b)^2.

  • Moment generating function

    The moment-generating function is: This shows how to find if a function is uniform.

  • Moment Generating Function and Expectation

    204427 Moment Generating Function and Expectation Please provide a solution for the following problem: Let Y denote a random variable with probability density function given by f(y) = (1/2)e ^-|y| , -∞ < y < ∞ Find the moment-generating

  • Moment Generating Function

    170703 Moment generating function What is the moment generating function of the probability density function f(x) = 4x-x^2 for 0

View More Related Solutions