MediumProbabilitypr-078

Order Statistic Density Value

Problem

Probability density of the k-th order statistic of n independent Uniform(0, 1) variables at x:

f_(k)(x) = n * C(n - 1, k - 1) * x^(k - 1) * (1 - x)^(n - k).

Return 0.0 when x is outside [0, 1] or k is outside 1..n.

Hint

Pick which observation lands at x, then order the rest around it.

case 1

in: [1,1,0.5]

expected: 1

case 2

in: [2,1,0.5]

expected: 1

case 3

in: [2,2,0.5]

expected: 1

case 4

in: [3,2,0.25]

expected: 1.125

case 5

in: [3,4,0.5]

expected: 0

Starter codePython

import math


def order_stat_density_value(n, k, x):
    # Your code here
    pass

5 test cases · run your code against them in the editor