 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/14/b/i/solution

Subtracting the constant translates the event without changing its probability. Therefore

P (a \leq U \leq b) = P (a - c \leq X \leq b - c) = \int_{a - c}^{b - c} f (x) d x .

This is a translation of the interval in the probability distribution of

X

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