Financial Risk Manager Part 1
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Let X have the following probability density function:
Calculate the mode of the distribution.
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Community
TTanishq
A
1.5
B
2.0
C
2.5
D
3.0
Explanation:
Solution
First, we need to find the value of C. Since this is a probability density function, the sum of all probabilities must equal 1:
Now we have the complete probability distribution:
- P(X=1) = 0.15
- P(X=2) = 0.25
- P(X=3) = 0.35
- P(X=4) = 0.25
The mode is the value with the highest probability in the distribution. Comparing the probabilities:
- P(X=1) = 0.15
- P(X=2) = 0.25
- P(X=3) = 0.35 (highest)
- P(X=4) = 0.25
Therefore, the mode is x = 3, which corresponds to option D.
Key Concept: The mode of a probability distribution is the value that occurs with the highest probability.
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