Problem: The following table gives the anticipated one-year rates of return from a certain investment and their associated probabilities.
Rate of Return X, % Probability,Pi
-20 0.10
-10 0.15
10 0.45
25 0.25
30 0.05
1) Calculate the expected rate of return, E(X).
2) Calculate the Variance and the Standard deviation of the returns.
3) What's the probability for this investment to yield a return of less than 10 %?
4) What's the probability for the returns of this investment to be between at least 10 % and at most 25 %?