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.

Answer 1

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