# Thread: variance of net return

1. ## variance of net return

A law firm is considering nominating to do work for the legal aid commission, but only if it is financially viable for them to do so. Based on historical data, if the defendant pleads guilty and a solicitor is only required for sentencing, then the firm's net return is $474. If the defendant pleads guilty, but the solicitor is also required during the giving of evidence, the net return is$150. On the other hand, if the defendant pleads not guilty then the net return is a LOSS of $504. If the probabilities for the first 2 scenarios are 0.34 and 0.48 respectively, then calculate the variance of the net return. I used the formula $Var(x) = \sum^{N}_{i=1} (x_{i}-\mu)^2 P(x_{i})$ but i got $Var(x) = 112624$ ??? this seems like a very large number... Oh and I got $E(x) = \mu = 142.66$... 2. Originally Posted by wik_chick88 A law firm is considering nominating to do work for the legal aid commission, but only if it is financially viable for them to do so. Based on historical data, if the defendant pleads guilty and a solicitor is only required for sentencing, then the firm's net return is$474. If the defendant pleads guilty, but the solicitor is also required during the giving of evidence, the net return is $150. On the other hand, if the defendant pleads not guilty then the net return is a LOSS of$504. If the probabilities for the first 2 scenarios are 0.34 and 0.48 respectively, then calculate the variance of the net return.

I used the formula $Var(x) = \sum^{N}_{i=1} (x_{i}-\mu)^2 P(x_{i})$

but i got $Var(x) = 112624$ ??? this seems like a very large number...

Oh and I got $E(x) = \mu = 142.66$...
Other than I make $\mu=142.44$ the variance is right.

CB