Distribution A: xi Distribution A: P(X=xi) Distribution B: xi Distribution B: P(X=xi) 0 0.03 0 0.49 1 0.08 1 0.23 2 0.17 2 0.17 3 0.23 3 0.08 4 0.49 4 0.03 What is the standard deviation for distribution B?
What is the standard deviation for distribution B?
0 0.49
1 0.23
2 0.17
3 0.08
4 0.03
Answer :
Given data is :
Distribution B is :
X | 0 | 1 | 2 | 3 | 4 |
P(X = x) | 0.49 | 0.23 | 0.17 |
0.08 |
0.03 |
E(X) =
= [(0 * 0.49) + (1 * 0.23) + (2 * 0.17) + (3 * 0.08) + (4 * 0.03)]
= [ 0 + 0.23 + 0.34 + 0.24 + 0.12]
= 0.93
E(X) = 0.93
therefore,
standard deviation =
where
=
= [0 + 0.23 + (4 * 0.17) + (9 * 0.08) + (16 * 0.03)]
= 0 + 0.23 + 0.68 + 0.72 + 0.48
= 2.11
so,
standard deviation =
=
=
=
=
Standard deviation for distribution B = 1.116
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