Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 16 / b

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- Solution b

Solution

The angular interval has width

π

, so its continuous uniform distribution has probability density function

g (θ) = {1/ π, 0, - π /2 < θ < π /2, otherwise .

Integrating this probability density function gives the cumulative distribution function

G (θ) = ⎩ ⎨ ⎧ 0, \frac{1}{2} + θ / π, 1, θ \leq - π /2, - π /2 < θ < π /2, θ \geq π /2.

Values of the probability density function at the two individual endpoints may be assigned arbitrarily without changing any probability.

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