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

E(X) = ∑xP(x)

= (3 × 0.2) + (4 × 0.3) + (5 × 05)

= 0.6 + 1.2 + 2.5

= 4.3

E(X²) = ∑x²P(x)

= (3² × 0.2) + (4² × 0.3) + (5² × 05)

= (9 × 0.2) + (16 × 0.3) + (25 × 0.5)

= 1.8 + 4.8 + 12.5

= 19.1

Variance of the Random Variable

σ² = Var(X) = E(X²) − (E(X))²

Var(X) = 19.1 − (4.3)²

= 19.1 − 18.49

= 0.61

Standard Deviation (σ)

σ = `sqrt(Var(X))`

= `sqrt0.61`

= 0.781