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 (S.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

∴ S.D. = `sqrt("Var"("X"))`

= `sqrt(0.49)`

= 0.7