Question

For the following distribution,

X: 0,1,2,3

P(x): 0.027, 0.189, 0.441, 0.343

What is the variance of the distribution?

2.1

0.63

3.9

2.754

Answer 1

Option B) 0.63

Explanation:

We are given the following in the question:

X: 0 1 2 3

P(x): 0.027 0.189 0.441 0.343

We have to find the variance for the given discrete probability distribution.

`E(X) = \displaystyle\sum x_iP(x_i)\\\\E(X) = 0(0.027) + 1(0.189) + 2(0.441) + 3(0.343)\\E(X) = 2.1\\\\E(X^2) = \displaystyle\sum x_i^2P(x_i)\\\\E(X^2) = 0^2(0.027) + 1^2(0.189) + 2^2(0.441) + 3^2(0.343)\\E(X^2) = 5.04\\\\Var(X) = E(X^2) -[E(X)]^2\\Var(X) = 5.04 - (2.1)^2\\Var(X) = 0.63`

The variance of given distribution is 0.63