Determine the kth percentile of the distribution defined by the following density function. f (x)= x...

Question

Question

Determine the kth percentile of the distribution defined by the following density function. f (x)= x o SxSVE O elsewhere

math Statistics-And-Probability

Answer 1

Answer #1

We want to find 'x' such that $P(X<x)=\frac{k}{100}$

$\\\int_{0}^{x}(x)dx=\frac{k}{100}\\ \\$

$[\frac{x^2}{2}]_{0}^{x}=\frac{k}{100}\\ \\$

$[\frac{x^2}{2}-0]=\frac{k}{100}\\ \\$

$\Rightarrow x=\sqrt{\frac{k}{50}}$

which is the k^th percentile.

Answer 2

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