a circumference arcsine law) 1 The projection X of the radius-vector of a random point on of radius a onto the diameter has the distribution function (the F(x) = + 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. TT x > a; a

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