(1) If there is a 20% chance we will get 16% return, a 30% chance of
getting a 14% return, a 40% chance of getting a 12% return, and a 10%
chance of getting an 8% return, what is the expected rate of return?
a)12%
b)13%
c)14%
d)15%

The standard deviation for the above investment would be:
a)2.24
b)2.56
c)2.83
d)2.98

Hi k9queen!!

Letīs go to work!!!

(1) If there is a 20% chance we will get 16% return, a 30% chance of
getting a 14% return, a 40% chance of getting a 12% return, and a 10%
chance of getting an 8% return, what is the expected rate of return?

This is "weight" problem:

Weight (or probability) of 16% return = W(16) = 0.2 ;
W(14) = 0.3 ;
W(12) = 0.4 ;
W(8)  = 0.1 .

Espected rate = W(16)*16 + W(14)*14 * W(12)*12 + W(8)*8=
              = 0.2*16 + 0.3*14 + 0.4*12 + 0.1*8 =
              = 3.2 + 4.2 + 4.8 + 0.8 =
              = 13%

The expected rate of return is 13% .

Note: this is a probabilistic problem where you calculate the Expected Value.
See at "Statistic Glossary" website the following page:
http://www.cas.lancs.ac.uk/glossary_v1.1/prob.html#expval



The standard deviation for the above investment:

First of all we must calculate the Variance:

If P(X) is the probability of X and E is the expected value, then
 
Var(X) = sum[(Xi-E)^2 * P(Xi)]  for i = 1 to n (in this case n = 4).
       = (16-13)^2 * 0.2 + (14-13)^2 * 0.3 + (12-13)^2 * 0.4 +
         + (8-13)^2 * 0.1 =
       = 3^2 * 0.2 + 1^2 * 0.3 + (-1)^2 * 0.4 + (-5)^2 * 0.1 =
       = 9 * 0.2 + 1 * 0.3 + 1 * 0.4 + 25 * 0.1 =
       = 1.8 + 0.3 + 0.4 + 2.5 =
       = 5

The standard deviation (s.d) is the square root of the variance, then

s.d = 5 ^ 1/2 =  2.24 .


I hope this helps, if you need a clarification, please post a request for it.

Thank you for your questions and the good ratings.

Best Regards.
livioflores-ga

Thank you! You are the best! And fastest!