Astick of length`is broken at a uniformly chosen random location. we denote the length of the smaller piece byx.(a) find the cumulative distribution function ofx.(b) find the probability density function ofx.

Answer and explanation

Step-by-step explanation:

Step one, defining the parameters

Let Cumulative distribution function be given by F(x) = P(X ≤ x)

Let the probability density function be given by f(x) = d/dxF(x)

Let U be the original length of the stick so that U≈U(o,w)

Let X be the length if the smaller piece of the stick so that X ≈ min { U, w-u}

The calculation is given in the attachment as I cannot insert formulas in here. This explanation will help you understand the calculation.