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A point (x, y, z) is chosen randomly inside a unit sphere so that the probability is uniform over all points in that sphere. a.

A point (x, y, z) is chosen randomly inside a unit sphere so that the probability is uniform over all points in that sphere.

a. Find the probability that the length from the origin to the chosen point is less than 1/2.

b. Find the probability density function for R, a random variable representing the distance from the origin to the point (x, y, z).

c. Find E[R].

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