Normalising a Two-Block Density — hard Random Variables problem | Incognition

Normalising a Two-Block Density

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Random VariablesHard

Normalising a Two-Block Density

A continuous random variable $X$ has a piecewise-constant probability density function built from two rectangular blocks:

$f(x) = 0.20$ for $0 \le x < 2$
$f(x) = c$ for $2 \le x \le 6$
$f(x) = 0$ everywhere else

The constant $c$ is whatever value makes $f$ a valid PDF.

What is $P(1 \le X \le 4)$ ?

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