Question

A random variable X has E(x) = 1/2 and E(x²) = 1/2 find its variance and standard deviation.

Answer 1

We have to use the formula,
Var(X) = E(x²) - [E(x)]²
Where Var(X) indicates variance of a random variable X .

Given,
E(X) = 1/2 and E(X²) = 1/2
∴ var(X) = 1/2 - 1/2² = 1/2 - 1/4 = 1/4
Hence, variance of a random variable X = 1/4

We also know ,
Standard deviation = √{variance} = √{1/4} = 1/2
Hence, standard deviation of a random variable X = 1/2