OBJECTIVES: This lab is designed to introduce you how to generate random  samples and show you how to generate a Binomial sample from a Bernoulli sample.

DIRECTIONS: Follow the instructions below, answering all questions. Your answers should be in the form of a brief report , to be handed in to the instructor before you leave.
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1.  DATA: Generate  a Bernoulli sample of size 1000 & probability of success =0.5.

    a. Calculate the mean & variance of your data.

    b.  Create a sample of 100 realizations of a Binomial random variable from
         your data. Calculate the mean of this sample.

    c.  Plot a relative frequency histogram for your binomial data & comment on it.

    d.  Compute the Binomial probability mass function ( from Calc ---> Probability Distributions  )
         and compare with part -c.

    e.  Compare the theoretical & observed means in part -b.
 

NOTE:  we can get 10 columns with 100 Bernoulli's in each column using the Stack/Unstack in the Manip menu .This requires creating a column of subscripts using  Calc---> Make patterned Data--->Simple Sets of Numbers.  One must then use Sum from Calc---> Row Statistics to get the Binomial observations.
 
 

2. DATA:  Generate a Binomial sample of size 1000  directly using "Random Data" in Calc menu & probability of success=0.5 .

   a. Calculate the mean  of your data & compare it with the theoretical mean .
 
   b.  Plot  a  relative frequency histogram for your data & comment on it. Compare with the
        probability mass function.

   c.  Repeat parts a.-b. after changing the sample size to 10,000.

   d.  Repeat parts a.-b. after  increasing the probability of success to  0.9.