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1 Poisson Distribution Exercise Set 1

This document contains 9 exercises involving calculating probabilities using the Poisson distribution. The Poisson distribution can model random processes where events occur continuously and independently at a certain average rate. The exercises involve calculating probabilities of events occurring in processes like phone calls arriving at an exchange, defects occurring in manufactured goods, and other scenarios where the average rates of occurrences are known.

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oliver sen
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58 views1 page

1 Poisson Distribution Exercise Set 1

This document contains 9 exercises involving calculating probabilities using the Poisson distribution. The Poisson distribution can model random processes where events occur continuously and independently at a certain average rate. The exercises involve calculating probabilities of events occurring in processes like phone calls arriving at an exchange, defects occurring in manufactured goods, and other scenarios where the average rates of occurrences are known.

Uploaded by

oliver sen
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1 Poisson Distribution

Exercise Set 1
1. Calls come in to a telephone exchange at random but at a rate of 300 per hour(when
taken over a long period). Assume that the number of calls coming in during a given
period is a random variable with a poisson distribution and determine the probability
that
(1) one call comes in during a given one-minute period.
(2) at least two calls come in during a given one-minute period.
(3) no calls arrive in an interval of length T minutes.
2. ’Joints’ in a certain manufactured tape occur at random, but on an average of one per
2000 feet. Assuming a Poisson distribution, what is the probability that a 5000-foot
roll of tape has
(1) no joints.
(2) at most two joints.
(3) at least two joints.
3. Flaws in gold plating of large sheets of metal occur at random, on the average of one
in each section of area 10 square feet. What is the probability that a sheet 5 by 8 will
have no flaws? At most one flaw?.
4. The numbers of arrivals of customers during any day follows Poisson distribution with
a mean of 5. What is the probability that the total number of customers on two days
selected at random is less than 2?
5. Suppose 3% of bolts made by a machine are defective, the defects occurring at random
during production. If bolts are packaged 50 per box, find exact probability and Poisson
approximation to it, that a given box will contain 5 defectives.
6. Using Poisson distribution, find the probability that the ace of spades will be drawn
from a pack of well-shuffled cards at least once in 104 consecutive trials.
7. If the probability that an individual suffers a bad reaction from a certain injection is
0.001, determine the probability that out of 2000 individuals
(1) exactly3,
(2) more than 2 individuals,
(3) none, (4) more than one individual will suffer a bad reaction.
8. In a certain factory turning out a razor blades, there is a small chance of 0.002 for
any blade to be defective. The blades are supplied in packets of 10, use appropriate
and suitable distribution to calculate the approximate number of packets containing
no defective, one defective and two defective blades respectively in a consignment of
50,000 packets.
9. A car hire firm has two cars which it hires out day by day. The number of demands
for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate
the number of days in a year on which
(1) car is not used. (2) the number of days in a year some demand is refused.
10. Suppose that a book of 600 pages contains 40 printing mistakes. Assume that these
errors are randomly distributed throughout the book and x, the number of error per
page has a Poisson distribution. What is the probability that 10 pages selected at
random will be free of errors?

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