Financial Risk Manager Part 1
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The yearly profits of the two firms A and B can be summarized in the following probability matrix.
| Company B (X₂) Profits | -1 Million (A) | 0 Million (A) | 2 Million (A) | 4 Million (A) |
|---|---|---|---|---|
| -50 Million | 0.01997 | 0.03995 | 0.010 | 0.002 |
| 0 Million | 0.03990 | 0.230 | 0.124 | 0.02998 |
| 10 Million | 0.011 | 0.127 | 0.144 | 0.06662 |
| 100 Million | 0 | 0.0309 | 0.06556 | 0.0618 |
What is the marginal distribution of company A?
Other
Community
NNikitesh
A
| Company A(X₁) Profits | -1 Million | 0 Million | 2 Million | 4 Million |
|---|---|---|---|---|
| P(X₁ = x₁) | 0.0697 | 0.4274 | 0.3436 | 0.1598 |
B
| Company A(X₁) Profits | -1 Million | 0 Million | 2 Million | 4 Million |
|---|---|---|---|---|
| P(X₁ = x₁) | 0.0697 | 0.5274 | 0.3436 | 0.0593 |
C
| Company A(X₁) Profits | -1 Million | 0 Million | 2 Million | 4 Million |
|---|---|---|---|---|
| P(X₁ = x₁) | 0.0697 | 0.5274 | 0.3436 | 0.0593 |
D
| Company A(X₁) Profits | -1 Million | 0 Million | 2 Million | 4 Million |
|---|---|---|---|---|
| P(X₁ = x₁) | 0.0697 | 0.5274 | 0.1235 | 0.2794 |
Explanation:
The marginal distribution of company A is obtained by summing the joint probabilities along the rows (across all values of X₂). From the given joint probability matrix:
For P(X₁ = -1M): 0.0197 + 0.0390 + 0.011 + 0 = 0.0697 For P(X₁ = 0M): 0.0395 + 0.230 + 0.127 + 0.0309 = 0.4274 For P(X₁ = 2M): 0.010 + 0.124 + 0.144 + 0.0656 = 0.3436 For P(X₁ = 4M): 0.002 + 0.0298 + 0.0662 + 0.0618 = 0.1598
These values match exactly with Table A, making it the correct marginal distribution.
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