You are Here: Home >< Maths

# Geometric distribution , cumulative from characteristic function watch

1. 1. The problem statement, all variables and given/known data

Hi, I have the probabilty density:

and I am asked to find the characteristic function:

and then use this to determine the mean and variance of the distribution.

2. Relevant equations

I have the general expression for the characteristic function :

* ,
from which can equate coefficients of to find the moments.

3. The attempt at a solution

So I have

I understand the solution given in my notes which is that this is equal to, after some rearranging etc, expanding out using taylor :

and then equating coefficients according to * However my method was to do the following , and I'm unsure why it is wrong:

And so comparing to *

Anyone tell me what I've done wrong? thank you, greatly appreciated.
2. (Original post by xfootiecrazeesarax)

I don't understand why the 2nd equality holds here (I am doubtful that it does...)
3. (Original post by DFranklin)
I don't understand why the 2nd equality holds here (I am doubtful that it does...)
expanded my exponential incorrectly, falling alseep, thank you !

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 11, 2017
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE