Financial Risk Manager Part 1
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Q.3744 The yearly profits of the two firms A and B can be summarized in the following probability matrix.
| Company B (X₂) | Company A Profits (X₁) | -1 Million | 0 Million | 2 Million | 4 Million |
|---|---|---|---|---|---|
| -50 Million | 0.0197 | 0.0395 | 0.010 | 0.002 | |
| 0 Million | 0.0390 | 0.230 | 0.124 | 0.0298 | |
| 10 Million | 0.011 | 0.127 | 0.144 | 0.0662 | |
| 100 Million | 0 | 0.0309 | 0.0656 | 0.0618 |
What is the marginal distribution of company B?
Explanation:
Explanation
To find the marginal distribution of Company B, we need to sum the probabilities across each row (for each value of Company B's profits).
Calculation:
For Company B = -50 Million: 0.0197 + 0.0395 + 0.010 + 0.002 = 0.0712
For Company B = 0 Million: 0.0390 + 0.230 + 0.124 + 0.0298 = 0.4228
For Company B = 10 Million: 0.011 + 0.127 + 0.144 + 0.0662 = 0.3482
For Company B = 100 Million: 0 + 0.0309 + 0.0656 + 0.0618 = 0.1583
Verification:
Total probability should sum to 1: 0.0712 + 0.4228 + 0.3482 + 0.1583 = 1.0005 (rounding error due to decimal precision)
Therefore, the correct marginal distribution for Company B is:
| Company B(X₂) Profits | -50 Million | 0 Million | 10 Million | 100 Million |
|---|---|---|---|---|
| P(X₂ = x₂) | 0.0712 | 0.4228 | 0.3482 | 0.1583 |
This matches Option C.