A random variable X is given by its distribution table:
X -10 5 10 20
P .15 .4 .35 .1
Find its variance and standard deviation.
Solution:
x | P(x) | x * P(x) | x2 * P(x) |
-10 | 0.15 | -1.5 | 15 |
5 | 0.4 | 2 | 10 |
10 | 0.35 | 3.5 | 35 |
20 | 0.1 | 2 | 40 |
Sum | 1 | 6 | 100 |
Mean =
X * P(X)
= 6
Standard deviation =
=X
2 * P(X) -
2
= 100
- (6)2 = 64
Standard deviation =
= 8
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