Financial Risk Manager Part 1
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The supermarket sells discounted items for an excellent price; this price is modeled uniformly on the interval [0,500]. Calculate the difference between the median and the 10th percentile.
Explanation:
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.