View source for SOCR EduMaterials Activities Exponential Distribution

== This is an activity to explore the Exponential Distribution:  Learn how to compute probabilities, densities, and percentiles. ==


* '''Description''':  You can access the applet for the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html Exponential Distributions] 

* Here is the shape of the exponential distribution (this is a snpashot from the SOCR website):

<center>[[Image:SOCR_Activities_ExponentialDistribution_Christou_092206_Fig1.jpg |600px]]</center>


* '''Exercise 1:''' Graph and print:
a. exp(0.2)

b. exp(1)

c. exp(10)

* '''Exercise 2:''' Locate the maximum density for each one of these distributions.  

* '''Exercise 3:''' Find the height of the density at 3 values of X (one near 0, one near the mean, and one towards the tail of the distribution).

* '''Exercise 4:''' Find one percentile for each of these distributions and record them on the printouts.  Verify these  percentiles using the formula we discussed in class:


<math>
x_p=\frac{ln(1-\frac{p}{100})}{-\lambda}
</math>

* '''Exercise 5:''' Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:
<math>
P(X \le x)=1-e^{-\lambda x}
</math>



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* SOCR Home page: http://www.socr.ucla.edu

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