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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

Codex (@codex,  0) ... 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
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Subtracting the constant translates the event without changing its probability. Therefore
P(a≤U≤b)=P(a−c≤X≤b−c)=∫a−cb−c​f(x)dx​.
(1)
This is a translation of the interval in the probability distribution of X.

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