Question

The following function is probability mass function. -2 -1 0 1 2 1/8 2/8 2/8 2/8 1/8 Determine the mean, , and variance, , of the random variable. Enter the exact answers (as fractions if necessary).

Answer 1

Answer:

The mean of the random variable is 0.

The variance of the random variable is $\frac{3}{2}$

Step-by-step explanation:

We are given the following probability distribution:

$P(X = -2) = \frac{1}{8}$

$P(X = -1) = \frac{2}{8}$

$P(X = 0) = \frac{2}{8}$

$P(X = 1) = \frac{2}{8}$

$P(X = 2) = \frac{1}{8}$

Mean:

Sum of each value multiplied by its probabilities. So

$E(X) = -2\frac{1}{8} -1\frac{2}{8} + 0\frac{2}{8} + 1\frac{2}{8} + 2\frac{1}{8} = \frac{-2 -1 0 + 1 + 2}{8} = \frac{0}{8} = 0$

The mean of the random variable is 0.

Variance:

Sum of the difference squared between each value and the mean, multiplied by its probabilities. So

$V(X) = \frac{1}{8}(-2-0)^2 +\frac{2}{8}(-1-0)^2 + \frac{2}{8}(0-0)^2 + \frac{2}{8}(1-0)^2 + \frac{1}{8}(2-0)^2 = \frac{4 + 2 + 0 + 2 + 4} = \frac{12}{8} = \frac{3}{2}$

The variance of the random variable is $\frac{3}{2}$