The projection X of the radius-vector of a random point on L a circumference of radius a onto the diameter has the distribution function (the arcsine law) F(x) { +arcsin for-a< x <6; Determine (a) the probability that X will be on the interval (-a/2, a/2), (b) the quantile x0.75, (c) the probability density f(x) of the random variable X, (d) the mode and median of the distribution.

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