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Question
The following table is describing about the probability mass function of the random variable X
| x | 3 | 4 | 5 |
| P(x) | 0.2 | 0.3 | 0.5 |
Find the standard deviation of x.
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Solution
Let x be the random variable taking the values 3, 4, 5
E(x) = Σpixi
= (0.1 × 3) + (0.1 × 4) + (0.2 × 5)
= 0.3 + 0.4 + 1.0
E(x) = 1.7
E(x2) = Σpixi2
= (0.1 × 32) + (0.1 × 42) + (0.2 × 52)
= (0.1 × 9) + (0.1 × 16) + (0.2 × 25)
E(x2) = 7.5
Var(x) = E(x2) – (E(x)]2
= 7.5 – (1.7)2
= 7.5 – 2.89
Var(x) = 4.61
Standard deviation (S.D) = `sqrt("var"(x))`
= `sqrt(4.61)`
σ = 2.15
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