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Answer: The probability matrix is a tabular representation of the probability mass function (PMF) which relates the outcomes of a bond's return profile and its classification.
## Explanation **B is correct.** The probability matrix is a tabular representation of a probability mass function (PMF) that relates the outcomes of a bond's return profile and its classification. ### Why B is correct: - A probability matrix displays joint probabilities for discrete random variables - It shows the probability of each combination of outcomes (return profile × classification) - This is the definition of a joint probability mass function (PMF) ### Why other options are incorrect: **A is incorrect:** The probability matrix represents a PMF, not a cumulative distribution function (CDF). A CDF shows cumulative probabilities up to certain values, while a PMF shows probabilities of specific outcomes. **C is incorrect:** Each cell contains the probability that a combination of **two** outcomes is realized (return profile and classification), not three outcomes. **D is incorrect:** The marginal distribution is computed by **summing** across rows or columns, not multiplying. For example, to get the marginal distribution of bond classifications, you would sum the probabilities across all return profiles for each classification type.
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A junior fixed-income analyst at an investment management firm is evaluating the credit quality of a diversified bond portfolio consisting of bonds classified as investment grade, high-yield, or unrated. Upon observing that the expected return profile of a bond appears to be related to its classification, the analyst constructs a probability matrix to assign probabilities to different combinations of a bond's return profile and its classification. Which of the following correctly describes this probability matrix?
A
The probability matrix is a multivariate representation of a cumulative density function (CDF) which relates the outcomes of a bond's return profile and its classification.
B
The probability matrix is a tabular representation of the probability mass function (PMF) which relates the outcomes of a bond's return profile and its classification.
C
Each cell in the probability matrix contains the probability that a combination of three outcomes is realized.
D
The marginal distribution of a random variable in the probability matrix can be computed by multiplying the probability of the three classification outcomes.
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