How Should I Calculate P(X<1.23) Using a Moment Generating Function?

[psycho007]

given m(t) = (1-p+p*e^t)^5
what is probability P(x<1.23)

i know that m(t) = e^tx * f(x)
m'(0) = E(X)
and m''(0) , can find the var(x)
should i calculate it using a normal table?

 

[Ray Vickson]

given m(t) = (1-p+p*e^t)^5
what is probability P(x<1.23)

i know that m(t) = e^tx * f(x)
m'(0) = E(X)
and m''(0) , can find the var(x)
should i calculate it using a normal table?

No, m(t) is not e^tx * f(x), but it is ∫{e^(tx) f(x) dx: x=0..∞}.

Why would you use a normal table when the random variable is very far from normal? You can actually work out explicitly what is the distribution by expanding out the power and collecting terms in e^(kt) for k = 0,1,2,3,4,5.

RGV