[ QUOTE ]
rata has obviously been corrected on the variances not being the same. They clearly have different variances, different standard deviations. Your really just averaging numbers (even tho their equity).
The distributions of the sample are different. They aren't the same at all.
Two samples:
0 1
.75 .75 0
They have the same mean, 0.50, they have different standard deviations/variances and distributions. If you plotted the 3 on a bar graph the two graphs would not be the same.
If you look at
http://en.wikipedia.org/wiki/Variance, scroll down to population variance and sample variance, there is a very clear formula:
variance=1/n*sum(xi-mean)^2
since we know the entire population of results (they are given), you don't need to use (n-1) as is used for samples.
So for the two samples:
variance1=1/2*((0-0.5)^2+(1-0.5)^2)=0.25
variance2=1/*
3 ((0.75-0.5)^2+(0.75-0.5)^2+(0-0.5)^2)=0.125
So the second example has half the variance as the first, which makes sense if you look at the two distributions.
I could look in my stats book and figure out the E(X) notation. I took another stats course which had the crap in it. But I don't see why I should bother.
edit: I made a mistake first time around, the 3 was a 2. It was calculated using 3 tho.
[/ QUOTE ]
Your and many others here are making the misstake of thinking that you can win a fraction of the pot. You always win 100% or 0% so the variance is the same.
And I have no idea why are you are referring to population variance and sample varince when we obviously know everything about the distribution.