Explanation:
The correct answer is A because when two marginal distributions are independent, the joint probability distribution is obtained by multiplying the corresponding marginal probabilities.
Explanation:
This concept is fundamental in probability theory and quantitative analysis, particularly when dealing with independent random variables in financial modeling.
Recall that if two marginal distributions are independent then:
f₍ₓ₁,ₓ₂₎(x₁, x₂) = f₍ₓ₁₎(x₁) f₍ₓ₂₎(x₂)
We are given the marginal distributions so that the joint distributions are given by multiplying their corresponding PMFs. For example, the joint probability that loan return is -20%, and the stock return is -5% is 30% × 40% = 12.
The other joint distributions are given in the table below:
| Loan | Return (X₁) | |
|---|---|---|
| –20% | 0% | |
| Stock | –5% | 12% |
| Market | 0% | 9.3% |
| Returns(X₂) | 9% | 7.7% |
A. Table A
B. Table B
C. Table C
D. Table D
A
Table A
B
Table B
C
Table C
D
Table D
