Combining Random Variables

Mattus

New Member
Hi All

Wonder if you can help. I apologise if this is basic but I am just learning Statistics and using the Khan Academy courses. I am a bit stuck when it comes to combining random variables. According to what I understand, you can add the means of 2 distributions and add the variances. However, if I produce small test distributions, I can show this doesn't work. For example:

Distribution A: 4,4,5,5,6,6,6,7 mean = 5.375 variance = 0.9844
Distribution B: 4,,5,5,5,5,7 mean = 5.167 variance = 0.8055

So based on what I have read, the combined mean should be 10.542, combined variance should be 1.7899

However, if I create Distribution C, by combining the values in A and B, I get 4,4,4,5,5,5,5,5,5,6,6,6,7,7 with mean 5.2857 and variance of 0.9183

So is my understanding incorrect that combining random variables is the same as combining the values into one distribution?

thanks

Matt

Last edited:

hlsmith

Not a robit
Not my area, but the sample sizes are different, so doesn't some type of weighting need to happen?

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BGM

TS Contributor
I guess the expected value and variance you quote is obtained by summing the two random variables, but what you are doing is mixing the two random variable to get a mixture. So they are not the same thing.

Mattus

New Member
Thanks, I see what you mean. I was thinking about this over the weekend and think I know where I went wrong