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In: Statistics and Probability

Choose a point at random from the unit square [0, 1] × [0, 1]. We also...

Choose a point at random from the unit square [0, 1] × [0, 1]. We also choose the second random point, independent of the first, uniformly on the line segment between (0, 0) and (1, 0). The random variable A is the area of a triangle with its corners at (0, 0) and the two selected points. Find the probability density function (pdf) of A.

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Answer:-

Given That:-

Choose a point at random from the unit square [0, 1] × [0, 1]. We also choose the second random point, independent of the first, uniformly on the line segment between (0, 0) and (1, 0). The random variable A is the area of a triangle with its corners at (0, 0) and the two selected points. Find the probability density function (pdf) of A.

Let the first point be denoted by

then

and

and denotes second point.

Area of triangle

If

Thus

Plz like it...,

orchestra answered 1 year ago

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