
Answer:
variance 0.163849748
Explanation:
[tex]\sum \frac{(x- mean)^2}{n}[/tex]
[tex]\left[\begin{array}{cccc}State&Return&Probability&Weight\\recession&0.2&-0.116&-0.0232\\fail&0.8&0.165&0.132\\Total&&0.049&0.1088\\\end{array}\right][/tex]
The mean average return will be 0.1088
(  (0.165 - 0.1088)² + (-0.116-0.1088)²  )  / 2  =
( 0,00315844 + 0,05053504‬ ) / 2 = 0,02684674‬
Now, we calcualate the root:
²√0,02684674‬ = 0.163849748