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A stick 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.

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udoikono

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.

${teks-lihat-gambar} udoikono

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