# Urgent Maclaurin Series/Stats Problem

Random Sampe of size n from distribution with pdf
f(x;p)={(lnp)^x}/px! for x=0,1,...; p>1 and 0 otherwise

Find CRLB for p?

My problem is finding E[x] which is somekind of maclaurin series but can't figure out which one?

Thanks

vela
Staff Emeritus
Homework Helper
I'm not familiar with the abbreviation CRLB. What does it mean?

What expression do you have for E[x]? You need to show more work for us to see where you're getting stuck.

E[x] = [1*(lnp)^1]/p*1!+[2*(lnp)^2]/p*2!+[3*(lnp)^3]/p*3!+....

Once I have the expected value E[X] of this distribution I will be able to find the CRLB as well which is defined to be in this case

1/(n*[d/dp ln f(x;p)]^2

Any help is appreciated

So my main problem is figuring out the E[X] and as a hint of this problem it is saying to use Maclaurin series.

Dick
Homework Helper
If you factor a 1/p out from your original f then you got z^k/k! (where I'm writing z=ln(p) and k=x to make it look more like a maclaurin series. Do you recognize what function that is? The expectation value is then associated with the maclaurin series k*z^k/k!=z^k/(k-1)!. Can you modify the function you recognized to get the second series?

sum of z^k/k! is e^k, so is it sum of z^k/(k-1)! will be e^(k-1)?

Dick