Phone calls arrive to your cell phone according to a Poissonprocess at rate 10 p
ID: 2917179 • Letter: P
Question
Phone calls arrive to your cell phone according to a Poissonprocess at rate 10 perhour.
(a) Let t3 denote the time of the 3rd call. Compute E(t3) and Var(t3),
(b) Given that exactly 5 calls came in during the 45 minute =3/4hour period
12:00{12:45AM, let K denote the number out of the 5 that came induring
the rst 15 minutes of this period. Find the probability massfunction for K;
P(K = k); 0 < k <= 5:
What kind of distribution is this?
(c) Continuation: What is the expected value E(K) and variance Var(K)?
(d) Given that exactly 1 call arrived during a given time interval(0; 2) (hours),
let 0 < t1 < 2 denote this arrival time. Compute thevariance, V ar(t1).
(e) Suppose that independently each call is either foreign (F) withprobability
p = 0:3 or domestic (D) with probability q = 0:7.
What is the expected number of D calls to come in during the hours1??3PM
given that there were 500 F calls in that very same period?
(f) Continuation: What is the probability that the rst 3 calls areD and the
fourth is F?
Explanation / Answer
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