 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/7/a/i/solution

Call the normalization constant

K

to distinguish it from the moment index used later. A probability density function must have total integral one, so

1 = K \int_{c}^{\infty} x^{- θ - 1} d x = \frac{K c ^{- θ}}{θ} .

Therefore $K = θ c^{θ}$ , the value denoted

k

in the density. This is the Pareto distribution with scale

c

θ

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