My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 14th, 2014, 04:43 PM   #1
Senior Member
 
Joined: Jan 2014

Posts: 196
Thanks: 3

Prob derived from mgf

If mgf of x

$\displaystyle m(t)=\frac{e^{5t}-e^{4t}}{t} , t\neq 0$ , $\displaystyle M(0)=1$
Find
a) $\displaystyle E(X)$
seems that $\displaystyle f(x)=1$ since
$\displaystyle \int_4^5 e^{tx}=\frac{e^{5t}-e^{4t}}{t}$
so
$\displaystyle \int_4^5 xdx=9/2$

b)$\displaystyle Var(X)$
$\displaystyle \int_4^5 x^2dx - 81/4=1/12$

c) find $\displaystyle P(4.2<x\leq 4.7)$

Any errors on a) & b)??

Not sure if I am approaching c) right.

Was thinking

$\displaystyle \int_{4.2}^{4.7}\frac{1}{4.7-4.2}dx$???

I think there is something I am missing on this part.
Thanks for any help!
WWRtelescoping is offline  
 
April 15th, 2014, 12:00 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,806
Thanks: 716

c) There is no reason to divide by 4.7 - 4.2. Since f(x) =1 in the interval [4,5], the probability is simply 4.7 - 4.2 = .5 (the integral of f(x) over the interval of interest).
mathman is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
derived, mgf, prob



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
I derived this rad function, but don't know what it means thefunctionofaperson New Users 2 June 12th, 2012 06:17 AM
How can this be derived? jackson_wang Calculus 1 November 30th, 2011 01:13 PM
Showing how the quadratic formlar was Derived-do you agree? dgoodman Algebra 0 September 30th, 2011 06:46 AM
Prob jpatche Advanced Statistics 1 February 26th, 2010 01:45 PM
Prob jpatche Algebra 1 February 26th, 2010 12:59 PM





Copyright © 2019 My Math Forum. All rights reserved.