Question

You are considering constructing a portfolio containing two assets F and G. Asset F will represent 40% of the value portfolio and asset G will account for the other 60%. The expected returns for each of these assets are shown below.
Probability of occurrence expected rates of return
F   G

0.1 6%   2%
0.2 8% 6%
0.4 10% 9%
0.2 12% 15%
0.1 14% 20%

Answer 1

So, what is the question? Your question has ended abruptly after the data, without specifying what needs to be done.

The typical questions for this kind of situation, is to calculate he expected return and standard deviation of the return of the portfolio.

I am proceeding with this assumption.

Probability	F	G	Rpi
Pi			0.4F + 0.6G
0.1	6%	2%	3.60%
0.2	8%	6%	6.80%
0.4	10%	9%	9.40%
0.2	12%	15%	13.80%
0.1	14%	20%	17.60%

Expected return of the portfolio, E(Rp) = Sum of (Pi x Rpi) = 0.1 x 3.60% + 0.2 x 6.80% + 0.4 x 9.40% + 0.2 x 13.80% + 0.1 x 17.60% = 10.00%

Variance of the return = Sum of [Pi x (Rpi - E(Rp))²] = 0.1 x (3.60% - 10.00%)² + 0.2 x (6.80% - 10.00%)² + 0.4 x (9.40% - 10.00%)² + 0.2 x (13.80% - 10.00%)²​​​​​​​ + 0.1 x (17.60% - 10.00%)²​​​​​​​ = 0.0014952

Hence, standard deviation of the expected return on the portfolio = Variance^1/2 =  0.038668 = 3.87%