4.34 Let X be a random variable with the following probability distribution: Find the standard deviation of X.

Complete question :

Let X be a random variable with the following probability distribution: Find the standard deviation of X.

X : - 2 ___ 3 5

P(x) __ 0.3 __ 0.2 ___ 0.5

3.04

Step-by-step explanation:

Given the data :

X : - 2 ___ 3 5

P(x) __ 0.3 __ 0.2 ___ 0.5

σ = √(Σ(x - μ)²*p(x))

μ = E = Σ(x*p(x)) = (-2*0.3) + (3*0.2) + (5*0.5) = 2.5

σ = √ ((-2 - 2.5)^2 * 0.3) + ((3 - 2.5)^2 * 0.2) + ((5 - 2.5)^2 * 0.5)

σ = √9.25

σ = 3.04138

σ = 3.04