An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year.
Return |
Probability |
-5 |
0.24 |
-8 |
0.30 |
10 |
0.15 |
12 |
0.11 |
-2 |
0.2 |
Find the standard deviation of this distribution. (Keep the answer with 2 decimal places)
Solution :
x | P(x) | x * P(x) | x^{2} * P(x) |
-5 | 0.24 | -1.2 | 6 |
-8 | 0.3 | -2.4 | 19.2 |
10 | 0.15 | 1.5 | 15 |
12 | 0.11 | 1.32 | 15.84 |
-2 | 0.2 | -0.4 | 0.8 |
Sum | 1 | -1.18 | 56.84 |
Mean = = X * P(X) = -1.18
Standard deviation =
=X ^{2} * P(X) - ^{2}
= 56.84 - (-1.18)^{2}
= 7.45
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