If X has the moment generating function
M(t) = (e^ ((PI)*t ) - e^ (et) ) / t
find E (X), V ar (X), and P (2.8 <= X < 3). help please?
What you need to do get E[X] is to evaluate the first derivative of M(t) at t=0.
$\displaystyle E[X]=\frac{d}{dt}M(0)$
For the variance, you need to find the second derivative of M(t) and E[X].
$\displaystyle Var(X)=E[X^2]-(E[X])^2=\frac{d^2}{dt^2}M(0)-(E[X])^2$
I hope that helps.
i got what i got before
1.24
http://www.wolframalpha.com/input/?i=(-e^2+%2B+pi^2)/2
the limit of the derivative of the mgf
as t approaches 0 is that function
and that function is not 1
oh wait, but thats allegedly the mean
i dunno, i don't think its a pdf