The annual profits (dividends, price gains) of 3 different securities 𝑊1, 𝑊2 and 𝑊3 are independ
Posted: Sun Sep 05, 2021 5:04 pm
The annual profits (dividends, price gains) of 3 different
securities 𝑊1, 𝑊2 and 𝑊3 are independent and normally distributed
with
𝑊1 ~ 𝑁 (10, 400), 𝑊2 ~ 𝑁 (20, 1500) and 𝑊3 ~ 𝑁 (50, 10000).
Investor 1 keeps 1 copy of 𝑊1 and 2 copies of 𝑊2 as a portfolio.
Investor 2 only holds 1 copy of 𝑊3. Then the probability is that
with the portfolio:
1 ) Investor 1 achieves a positive profit, higher than for
investor 2, true or false
2) Investor 1 achieved a profit of more than 100 euros, higher
than for investor 2. true or false
Tip: the expected values of the portfolios are the same (namely
=?); then only variances are decisive; possibly sketch
densities
securities 𝑊1, 𝑊2 and 𝑊3 are independent and normally distributed
with
𝑊1 ~ 𝑁 (10, 400), 𝑊2 ~ 𝑁 (20, 1500) and 𝑊3 ~ 𝑁 (50, 10000).
Investor 1 keeps 1 copy of 𝑊1 and 2 copies of 𝑊2 as a portfolio.
Investor 2 only holds 1 copy of 𝑊3. Then the probability is that
with the portfolio:
1 ) Investor 1 achieves a positive profit, higher than for
investor 2, true or false
2) Investor 1 achieved a profit of more than 100 euros, higher
than for investor 2. true or false
Tip: the expected values of the portfolios are the same (namely
=?); then only variances are decisive; possibly sketch
densities