Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.8 Probability and Integration - Exercises - Page 448: 10


$1$; $p(t)$ satisfies the given condition.

Work Step by Step

Let us consider for any $r \gt 0$: $I=\int_{0}^{\infty} (\dfrac{1}{r}) e^{-t/r} \ dx \\=(\dfrac{1}{r}) \lim\limits_{a \to \infty} \int_0^a e^{-t/r} \ dt \\=\dfrac{1}{r} \lim\limits_{a \to \infty} (-r) [e^{t/r}]_0^a\\=\\=(-1)(-1)\\=1$ This implies that $p(t)$ satisfies the given condition.
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