Conditioning (probability) - Conditioning On The Level of Measure Theory

Conditioning On The Level of Measure Theory

Example. Let Y be a random variable distributed uniformly on (0,1), and X = f(Y) where f is a given function. Two cases are treated below: f = f1 and f = f2, where f1 is the continuous piecewise-linear function

f_1(y) = \begin{cases} 3y &\text{for } 0 \le y \le 1/3,\\ 1.5(1-y) &\text{for } 1/3 \le y \le 2/3,\\ 0.5 &\text{for } 2/3 \le y \le 1, \end{cases}

and f2 is the Weierstrass function.

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