You are given the probability distribution below:
x | 0 | 1 | 2 | 3 | 4 |
p(x) | 0.05 | 0.35 | 0.25 | 0.20 | 0.15 |
Determine the standard deviation of X. Report your answer to three decimal places.
Solution:
We have
Mean = ∑XP(X)
Variance = ∑ P(X)*(X - mean)^2
Standard deviation = Sqrt(Variance)
The calculation table is given as below:
X |
P(X) |
XP(X) |
P(X)*(X - mean)^2 |
0 |
0.05 |
0 |
0.210125 |
1 |
0.35 |
0.35 |
0.385875 |
2 |
0.25 |
0.5 |
0.000625 |
3 |
0.2 |
0.6 |
0.1805 |
4 |
0.15 |
0.6 |
0.570375 |
Total |
1 |
2.05 |
1.3475 |
Mean = 2.05
Variance = 1.3475
Standard deviation = sqrt(1.3475) = 1.160818677
Standard deviation = 1.161
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