a. Given an arrival process with λ= 8.0, what is the probability that an arrival occurs...
a. Given an arrival process with λ= 8.0, what is the probability that an arrival occurs in the first t = 7 time units?
b. Given an arrival process with λ= 5.0, what is the probability that an arrival occurs after t = 5 time units?
Homework Answers
Answer:
Given that:
a) Given an arrival process with λ= 8.0, what is the probability that an arrival occurs in the first t = 7 time units?
An arrival process with 
. Let T be time of an arrival
Where 
is a rate parameter
CDF of T is
The probability that an arrival occurs in the first t = 7 times units given by
b) Given an arrival process with λ= 5.0, what is the probability that an arrival occurs after t = 5 time units?
An arrival process with 
. Let T be time of an arrival
Where
is a rate parameter
CDF of T is
The CDF provided is incorrect since 5.0 is the value of the rate parameter not the value of mean arrivals. If we have given the mean arrivals we used (1/0.5)
Therefore the probability that an arrival occurs after t=5 time units is given by
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