Pearson eText for Probability & Statistics for Engineers and Scientists with R -- Instant Access (Pearson+)
1st Edition
ISBN: 9780137548552
Author: Michael Akritas
Publisher: PEARSON+
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f E and F are disjoint events, P(E and F) =
Find the cdf of a random variable Y whose pdf is given by;
2, 0≤x≤1
1/3, 0≤x≤1
a) f(x)=3, 2≤x≤4
0, elsewhere
2, 1≤x≤2
b) f(x)=
(3-x)2, 2≤x≤3
0, elsewhere
There are m users who share a computer system. Each user alternates between "thinking" intervals whose durations are
independent exponentially distributed with parameter Y, and an "active" mode that starts by submitting a service re-
quest. The server can only serve one request at a time, and will serve a request completely before serving other requests.
The service times of different requests are independent exponentially distributed random variables with parameter μ,
and also independent of the thinking times of the users. Construct a Markov chain model and derive the steady-state
distribution of the number of pending requests, including the one presently served, if any.
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