Financial Risk Manager Part 1

Explanation

For a uniform distribution on the interval [0,500], the probability density function is:

[ f(x) = \frac{1}{500 - 0} = \frac{1}{500} ]

Finding the Median (50th percentile)

The median is found by solving: [ P(X < k) = (k - 0) \cdot f(x) = 0.5 ] [ \Rightarrow \frac{1}{500}k = 0.5 ] [ \Rightarrow k = 0.5 \times 500 = 250 ]

Finding the 10th percentile

The 10th percentile is found by solving: [ P(X < k) = (k - 0) \cdot f(x) = 0.10 ] [ \Rightarrow \frac{1}{500}k = 0.10 ] [ \Rightarrow k = 0.10 \times 500 = 50 ]

Calculating the Difference

[ \text{Difference} = \text{Median} - \text{10th percentile} = 250 - 50 = 200 ]

Therefore, the correct answer is B. 200.