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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: 6,806 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).


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