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.

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TTanishq

250

200

240

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.

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