 Solution

ID: 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/solution

The angular interval has width

π

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

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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