Question

For the following probability distribution, determine standard deviation of the random variable X.

| X | 2 | 3 | 4 |
| P(X) | 0.2 | 0.5 | 0.3 |

Answer 1

We know that: Standard deviation ( *.D.) = $sqrt("Variance")$

Var(X) = E(X2) [E(X)]2

E(X) = 2 0.2 + 3 0.5 + 4 0.3

= 0.4 + 1.5 + 1.2

= 3.1

E(X2) = 4 0.2 + 9 0.5 + 16 0.3

= 0.8 + 4.5 + 4.8

= 10.1

So V(X) = 10.1 (3.1)2

= 10.1 9.61

= 0.49

*.D. = $sqrt("Var"("X"))$

= $sqrt(0.49)$

= 0.7