Respuesta :
Answer:
[tex] E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%[/tex]
Now we can find the second central moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i) [/tex]
And replacing we got:
[tex]E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965[/tex]
And the variance is given by:
[tex] Var(X) = E(X^2) - [E(X)]^2[/tex]
And replacing we got:
[tex] Var(X) = 413.5965 -(11.759)^2 =275.5105[/tex]
And finally the deviation would be:
[tex] Sd(X) = \sqrt{275.5105}= 16.599 \%[/tex]
Step-by-step explanation:
We can define the random variable of interest X as the return from a stock and we know the following conditions:
[tex] X_1 = 23.4 , P(X_1) =0.67[/tex] represent the result if the economy improves
[tex] X_2 = -11.9 , P(X_1) =0.33[/tex] represent the result if we have a recession
We want to find the standard deviation for the returns on the stock. We need to begin finding the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i) [/tex]
And replacing the data given we got:
[tex] E(X) = 23.4* 0.67 -11.9*0.33= 11.759 \%[/tex]
Now we can find the second central moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i) [/tex]
And replacing we got:
[tex]E(X^2) = (23.4)^2* 0.67 +(-11.9)^2*0.33= 413.5965[/tex]
And the variance is given by:
[tex] Var(X) = E(X^2) - [E(X)]^2[/tex]
And replacing we got:
[tex] Var(X) = 413.5965 -(11.759)^2 =275.5105[/tex]
And finally the deviation would be:
[tex] Sd(X) = \sqrt{275.5105}= 16.599 \%[/tex]
