https://training-course-material.com/index.php?action=history&feed=atom&title=Poisson_DistributionPoisson Distribution - Revision history2026-05-13T12:24:54ZRevision history for this page on the wikiMediaWiki 1.45.1https://training-course-material.com/index.php?title=Poisson_Distribution&diff=17255&oldid=prevBernard Szlachta: /* Quiz */2014-05-29T13:16:30Z<p><span class="autocomment">Quiz</span></p>
<p><b>New page</b></p><div>{{Cat|Probability| 05}}<br />
== Poisson Distribution ==<br />
[[File:Poisson pmf.svg]]<br />
* calculating randomly scattered events in time or in space<br />
; Examples<br />
* number of road accidents in given period<br />
* goals scored in a soccer match<br />
* number of Losses/Claims occurring in a given period<br />
* number of customers calling in a day<br />
<br />
== Formula ==<br />
*In order to apply the Poisson distribution, the various events must be independent. <br />
General formula of Poisson distribution is:<br />
[[File:ClipCapIt-140526-182302.PNG]]<br />
e is the base of natural logarithms (2.7183)<br />
μ is the mean number of "successes"<br />
x is the number of "successes" in question<br />
<br />
==Example==<br />
Suppose you knew that the mean number of customer calls to your company on a weekday is 8. <br />
* What is the probability that on a given weekday there would be 11 calls? <br />
* This problem can be solved using the following formula based on the Poisson distribution:<br />
[[File:ClipCapIt-140526-182254.PNG]]<br />
In a spreadsheet<br />
=POISSON(11,8,false)<br />
since the mean is 8 and the question pertains to 11 calls.<br />
<br />
*The mean of the Poisson distribution is μ. <br />
*The variance is also equal to μ. <br />
*Thus, for this example, both the mean and the variance are equal to 8.<br />
<br />
=Quiz=<br />
<quiz display=simple><br />
<br />
{The mean number of defective products produced in a factory in one day is 21. What is the probability that in a given day there are exactly 12 defective products?<br />
<br />
|type="{}"}<br />
{ 0.012 | .012 }<br />
<br />
{<br />
{{Show Answer|<br />
0.012<br />
<br />
0.012 can be obtained using the formula.<br />
}}<br />
}<br />
<br />
<br />
{Which of these can be computed using Poisson distribution?<br />
|type="[]"}<br />
-average waiting time between phone calls<br />
+number of people killed accidentally by horse kicks<br />
<br />
{Which of these can be computed using Poisson distribution?<br />
|type="[]"}<br />
+number of enquiries via online form in a month<br />
-probability of selecting a person over 2 meter high</div>Bernard Szlachta