Untitled Document

SOME DISCRETE DITRIBUTIONS

Binomial	Geometric	Hypergeometric	Poisson
n identical trials	Do the experiment until you get the first success	Draw n elements without replacement from a set of N elements, r of which are successes and (N-r) of which are failures
Two possible outcomes; S="success" F="failure"	Two possible outcomes; S="success" F="failure"
p=P("success") is the same from trial to trial	p=P("success") is the same from trial to trial		Probability that an event occurs in a given unit is the same for all units
independent trials	independent trials		The number of events in one unit is independent of the number that occur in other units
X="the number of successes in n trials"	X="the number of trials on which the first success occurs"	X="the number of successes in the draw of n elements"	X="the number of times an event occurs in a given unit"

ACTIVITY 1.

Generating Observations from Binomial Distribution

Step 1: Click on the "Generate" button on the Statlets window at the end of this page.
Step 2: Click on the "Random numbers" button.
Step 3: Click on the "Binomial" button and type 60 in the "Sample size" box.
Step 4: Click on the "OK" button.
Step 5: Type 0.5 in the left window that appears, this is the p=P("success"), and type 10 in the right window, this is the n. Click "OK".
Step 6: Select the "Histogram" from menu options.

Repeat the above steps for p=0.8, then for p=0.2. Comment on the shape of the histogram for these three values of p.

ACTIVITY 2.

Generating Observations from Geometric Distribution

Step 1: Click on the "Generate" button on the Statlets window at the end of this page.
Step 2: Click on the "Random numbers" button.
Step 3: Click on the "Geometric" button and type 60 in the "Sample size" box.
Step 4: Click on the "OK" button.
Step 5: Type 0.5 in the window that appears, this is the p=P("success"). Click "OK".
Step 6: Select the "Histogram" from menu options.

Repeat the above steps for p=0.8, then for p=0.2. Comment on the shape of the histogram for these three values of p.

ACTIVITY 3.

Generating Observations from Hypergeometric Distribution

Step 1: Click on the "Generate" button on the Statlets window at the end of this page.
Step 2: Click on the "Random numbers" button.
Step 3: Click on the "Hypergeometric" button and type 60 in the "Sample size" box.
Step 4: Click on the "OK" button.
Step 5: Type 20 in the left window that appears, this is the N=population size, type 10 in the middle window, this is the r=the number of successes in the population, and type 9, this is the n=sample size. Click "OK".
Step 6: Select the "Histogram" from menu options.

Repeat the above steps for r=15, then for r=3. Comment on the shape of the histogram for these three values of r.

ACTIVITY 4.

Generating Observations from Possion Distribution

Step 1: Click on the "Generate" button on the Statlets window at the end of this page.
Step 2: Click on the "Random numbers" button.
Step 3: Click on the "Poisson" button and type 60 in the "Sample size" box.
Step 4: Click on the "OK" button.
Step 5: Type 12 in the box that appears, this is the mean of the Poisson distribution. Click "OK".
Step 6: Select the "Histogram" from menu options.

Repeat the above steps for mean=5, then for mean=100. Comment on the shape of the histogram for these three values of the mean.