# Expected value and Standard deviation of 2 alternatives

#### Jeremy87

##### New Member
Hi! I'm glad I found this great forum! I really hope to be of use myself and help answer some easier questions. In the meantime, could somebody please help me out with this one? I think I get it right, but I'm not 100% sure.

You are offered two alternative investments (the required amount being 10000 €). Both of them include some level of incertitude. The following table shows the possible gains/losses and their estimated probabilities.

Alternative 1: Profit -4000 Probability 10%, Profit 1000 Probability 90%
Alternative 2: Profit -250 Probability 40%, Profit 1000 Probability 90%

Question 1: Let us assume that the outcomes of these alternatives are independent. If you invest 10000 € in each of them, what is the expected total profit and what is the corresponding standard deviation?

Question 2: Let us assume that you decide to invest 10000 €. You choose either one of the alternatives arbitrary.
a) What is your expected profit and its standard deviation?

Let us assume that two investors choose an investment alternative independently of each other.
b) What is their expected combined profit and its standard deviation?

Question 1:

Expected value of alternative 1 = 1500
std.dev. = 500

Expected value of alternative 2 = 612.37
std.dev. = 500

Expected profit 1500 + 612.37= 2112.37
Expected std.dev. = 500 + 500 = 1000

Question 2:
a)
Expected profit:
(1/2)*((-4000*0.1)+(1000*0.9))+(1/2)*((-250*0.4)+(1000*0.6))= 500

Standard deviation:
(1/2)*((-4500)^2*0.1)= 1012500
(1/2)*((1000)^2*0.9))= 450000
(1/2)*((-250^2*0.4)= 12500
(1/2)*(1000^2*0.6))= 300000

=1012500+450000+12500+300000=1775000
SQRT(1775000)= 1332.291

b)
Expected profit:
(1/2)*((-8000*0.1)+(2000*0.9))+(1/2)*((-500*0.4)+(2000*0.6))= 1000

Standard deviation:
(1/2)*((-9000)^2*0.1)= 4050000
(1/2)*((2000)^2*0.9))= 1800000
(1/2)*((-500^2*0.4)= 50000
(1/2)*(2000^2*0.6))= 1200000

= 4050000+1800000+50000+1200000= 7100000
SQRT(7100000)= 2664.583

What do you think? Is this the right way to do this?