Question

Consider the following data x -4,-3,-2-1,0 P(X=x) 0.2,0.1,0.2,0.1,0.4Find the variance. Round your answer to one decimal place

Answer 1

First, we need to find the mean of the given values. This is given as

`\begin{gathered} \mu=(-4-3-2-1+0)/(5) \\ \mu=(-10)/(5) \\ \mu=-2 \end{gathered}`

once we have the mean, the variance is given as

`\text{Var}=\sum ^5_(j\mathop=1)x^2_j\cdot P_j-\mu^2`

where P_j denotes the probability of the j-place . In our case, we have

`\text{Var}=\lbrack(-4)^2\cdot0.2+(-3)^2\cdot0.1+(-2)^2\cdot0.2+(-1)^2\cdot0.1+(0)^2\cdot0.4\rbrack-(-2)^2`

which gives

`\begin{gathered} \text{Var}=\lbrack16\cdot0.2+9\cdot0.1+4\cdot0.2+1\cdot0.1\rbrack-4 \\ \text{Var}=5-4 \\ \text{Var}=1 \end{gathered}`

the answer is variance = 1