Question

The value of the expected value is -2.1. I need to know the variance. Here is a picture including the graph.

Answer 1

Given that

The table consists of probability distribution x and P(x) as

Explanation -

The formula for the variance is

`\begin{gathered} Var=\sigma^2=\sum_{x\mathop{=}-4}^0x^2* P(x)-\mu^2 \\ where\text{ }\mu\text{ is the standard deviation } \\ \mu=\sum_{x\mathop{=}-4}^0x* P(x) \end{gathered}`

So on substituting the values we have

`\begin{gathered} \mu=-4*0.2+(-3)*0.3+(-2)*0.1+(-1)*0.2+(0)*0.2 \\ \mu=-0.8-0.9-0.2-0.2+0 \\ \mu=-2.1 \\ and \\ \sigma^2=16*0.2+9*0.3+4*0.1+1*0.2+0-4.41 \\ \sigma^2=6.5-4.41=2.09 \end{gathered}`

Hence, the variance is 2.09.

And the final answer is 2.09