Question

Find the variance of the following data. Round the answer to one decimal place.

Answer 1

For this case we have the following info:

x -4 -3 -2 -1 0 1

P(X) 0.2 0.1 0.1 0.2 0.1 0.3

We can find the variance with this formula:

`\text{Var(X)}=E(X^2)-\lbrack E(X)\rbrack^2`

We can find the expected value like this:

`E(X)=\sum ^n_(i=1)x_iP(X_i)=-4\cdot0.2-3\cdot0.1-2\cdot0.1-1\cdot0.2+0\cdot0.1+1\cdot0.3^{}`

Solving we got:

E(X)= -1.2

The second moment is given by:

`E(X^2)=\sum ^n_(i=1)x^2_iP(X_i)=16\cdot0.2+9\cdot0.1+4\cdot0.1+1\cdot0.2+0\cdot0.1+1\cdot0.3`

Solving we got:

E(X^2)= 5

Solving we got:

`\text{Var(X)}=5-(-1.2)^2=3.56`

Rounded to one decimal place we got:

3.6