Financial Risk Manager Part 1

The correct answer is Table A.

Explanation:

A marginal distribution gives the probability distribution of a single variable from a joint distribution, obtained by summing the joint probabilities over all possible values of the other variable(s).

In this case, for a bivariate distribution, the marginal PMF of X₁ (Company A) is computed by summing up the probabilities for X₁ across all the values at which X₂ (Company B) is realized.

For example, the first probability P(X₁ = -1M) would be calculated by summing all joint probabilities where X₁ = -1M across all values of X₂.

Key characteristics of a valid marginal distribution:

1. All probabilities must be between 0 and 1
2. The sum of all probabilities must equal 1

Let's verify Table A:

• 0.0697 + 0.4274 + 0.3436 + 0.1598 = 1.0005 (approximately 1, accounting for rounding)
• All values are valid probabilities between 0 and 1

Table A represents the correct marginal distribution for Company A, as it satisfies the fundamental properties of a probability distribution.