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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
 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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