Question

# Q1.    Select an arrival (Poisson) process on any time interval (eg.: second, minute, hour, day, week,...

Q1.    Select an arrival (Poisson) process on any time interval (eg.: second, minute, hour, day, week, month, etc….) as you like.

Possible arrival processes could be arrival of signal, click, broadcast, defective product, customer, passenger, patient, rain, storm, earthquake etc.[Hint: Poisson and exponential distributions exits at the same time.]

Collect approximately n=30 observations per unit time interval. .[Hint: Plot your observations. If there is sharp increase or decrease then you could assume that you are observing arrivals according to proper Poisson process. For example: when scheduled flight time approaches number of passengers arriving to the check-in increases. It is the same for arrival of students to the classroom]

Use this data to estimate l of Poisson distribution. Estimate o l denoted by λ=SXi/n (average of observations)

1. What is the probability that we will observe (2* λ) arrivals in less than three unit time.

Since we have given that

n =

and say

So, the mean would become :

a) probability that we will observe (2* λ) arrivals in less than three unit time.

First,

Now,

So, it becomes:

b) the probability of less than three unit time is 0.0589.

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