You are Here: Home >< Maths

1. If x1~geometric(0.2) and x2~(0.4) what is the moment generating function of 2x1+4x2 and does 2x1+4x2 have geometric distribution?
2. (Original post by Harriettttttt1)
If x1~geometric(0.2) and x2~(0.4) what is the moment generating function of 2x1+4x2 and does 2x1+4x2 have geometric distribution?
So the definition of the moment generating function is

If you do the sums you will find that for a geometric distribution with parameter p, this is

(provided that you're using the geometric distribution with support on the strictly positive integers)

To answer the next part, how do you work out the moment generating function of aX + bY (a, b integer constants) from those of X & Y? You should know a theorem that helps you with this. Then finally, is the MGF that you obtain in the form of the MGF of some geometric distribution?

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: April 22, 2016
Today on TSR

### Tuition fees under review

Would you pay less for a humanities degree?

### Buying condoms for the first time - help!

Discussions on TSR

• Latest
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
Discussions on TSR

• Latest

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