(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1, 2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0. You are waiting for either bus 1 or 2 to arrive. Let W denote the waiting time until you can get on a bus. i. Explain briefly why W min(T, T). ii. Show that E(W) < 1/max(\1, A2). (Hint: You need to work out E(T¡) and E(T,) first.) ii. Work out the probability density function of W. (Hint: Find P(W > w) first for w > 0.)
(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1, 2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0. You are waiting for either bus 1 or 2 to arrive. Let W denote the waiting time until you can get on a bus. i. Explain briefly why W min(T, T). ii. Show that E(W) < 1/max(\1, A2). (Hint: You need to work out E(T¡) and E(T,) first.) ii. Work out the probability density function of W. (Hint: Find P(W > w) first for w > 0.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1, 2,
the waiting time until bus i arrives is denoted by T;, with T independent of T2,
and T; has density function
fr. (t) = X, exp(-1;t), t>0.
You are waiting for either bus 1 or 2 to arrive. Let W denote the waiting time until
you can get on a bus.
Transcribed Image Text:i. Explain briefly why W
min(T, T).
ii. Show that E(W) < 1/max(\1, A2). (Hint: You need to work out E(T¡) and
E(T,) first.)
ii. Work out the probability density function of W. (Hint: Find P(W > w) first
for w > 0.)
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