Question

A market research team compiled the following discrete probability distribution, where X represents the number of automobiles owned by a family residing in Montgomery County, and P(X) is the probability.

x P(x)

0- 0.3,

1- 0.5,

2- 0.2,

3- 0.4

The standard deviation of X is

Answer 1

The standard deviation of X is 0.7

Explanation:

We are given the following distribution:

x: 0 1 2 3

P(x): 0.3 0.5 0.2 0.4

We have to find the standard deviation of X.

Formula:

`E(x) = \displaystyle\sum x_iP(x_i)\\\\E(x) =0(0.3) + 1(0.5) + 2(0.2) + 3(0.4)\\\\E(x) = 2.1\\\\E(x^2) = \displaystyle\sum x_i^2P(x_i)\\\\E(x^2) =0(0.3) + 1(0.5) + 4(0.2) + 9(0.4)\\\\E(x^2) = 4.9\\\\Var(x) = E(x^2) - (E(x))^2 = 4.9-(2.1)^2 = 0.49\\\\\sigma(x) = √(Var(x)) =√(0.49) = 0.7`

Thus, the standard deviation of X is 0.7