
Advanced Statistics Advanced Probability and Statistics Math Forum 
 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 $\displaystyle \int_{4.2}^{4.7}\frac{1}{4.74.2}dx$??? I think there is something I am missing on this part. Thanks for any help! 
April 15th, 2014, 12:00 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,727 Thanks: 688 
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).


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 Deriveddo 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 