Combining Random Variables

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?


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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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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.