3  Variance of a random variable
The mean of a random variable does not give us information about the variability in the
values of the random variable In fact, if the variance is small, then the values of the
random variable are close to the mean Also random variables with different probability
distributions can have equal means, as shown in the following distributions of X and Y X
1
2
3
4
P(X)
1
8
2
8
3
8
2
8
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MATHEMATICS
Y
–1
0
4
5
6
P(Y)
1
8
2
8
3
8
1
8
1
8
Clearly
E(X) =
1
2
3
2
22
1
2
3
4
2