The projection X of the radius-vector of a random point on a circumference of radius a onto the diameter has the distribution function (the arcsine law) (x > a; F(x) 1 + arcsin for-a< x < a; (x ≤-a. 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. ४/०

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