You are Here: Home >< Maths

# Conbination of Random Variables - S3

1. Hi, I know this has probably been asked a lot, but I don't really understand it.
When combining random variables there are two cases, and I don't really understand when to use one case and when to use another, I don't think the S3 book explains it very well.
(i) E(aX +bY), Var(aX + bY) = aE(X) + bE(X), (a^2)Var(X) + (a^2)Var(Y)
(ii) But for linear combinations where X~N(mu1, sigmasquared1), Y~N(mu2, sigmasquared2),
aX +bY ~N(a*mu1 + b*mu2, a*sigmasquared1 + b*sigmasquared2)

Any help would really be appreciated,
thanks
Charlie
2. (Original post by charlie2434)
Hi

I'm trying to ignore the formulae you've written because reading non-LaTeX stuff hurts my eyes

I think what you are referring to is when you've got multiple cases of one variable vs one case of one variable multiplied several times.

If you have loads of observations, the errors tend to sort themselves out. As in, some will deviate to be higher than the mean, but some will deviate to be lower than the mean and the errors cancel. Whereas if you take one observation and multiply it, the error is amplified. So that's where the different formulae come from.

eg 50 observations of bolt sizes will be distributed with a variance of 50σ2 whereas 50b, where b is the observation of one bolt size, will be distributed with a variance of 502σ2, IIRC.
eg 50 observations of bolt sizes will be distributed with a variance of 50σ2 whereas 50b, where b is the observation of one bolt size, will be distributed with a variance of 502σ2, IIRC.
This is correct. In the exam it's more common to be given the former -- if you are really unsure then just check what your value of the variance is for both. A high variance usually means you've done something wrong.
4. (Original post by Zhy)
This is correct. In the exam it's more common to be given the former -- if you are really unsure then just check what your value of the variance is for both. A high variance usually means you've done something wrong.
Ah good. Was trying to come up with a simple example.

Also, OP - normally, you'll use this in conjunction with a hypothesis test, so you could check your end result - does it look right that you're rejecting/accepting the null hypothesis? If it doesn't, then either you've got an odd significance level, or you've done something wrong.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 7, 2012
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:
Today on TSR

### Help!

Will Oxford nullify my offer?

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