mcfarland, 22sep2000


UCLA Soc. 210a, Assignment 4:  

Probability


These exercises cover preliminary aspects of probability, random
variables, and distributions. Postponed to Assignment 5 are:
conditional probability, independence, Bayes' Rule, and related
matters.


1.  After reading Moore and McCabe pp 295-301 (part of Section
4.2), do the following exercises beginning on page 306:
	4.15, 4.21, 4.23, 4.25, 4.27, 4.31


2.  Consider the universal set that consists of 100 people, whose
gender and politics are as follows:
                  Conservative   Liberal
        Male          10           30
        Female        20           40

How many people are in each of the following subsets?

        universal set
        males
        females
        conservatives
        liberals
        male liberals
        female liberals
        male conservatives
        female conservatives
        empty set


3. (Continuation) If one person is chosen at random (i.e., in
such a manner that each of the 100 has the same probability of
being chosen), find the probability that the one person chosen
will be:

        male liberal
        female
        conservative
        female liberal


4.  Begin a new stata session.  Create 10 random digits as
follows:
        set obs 10
        generate x1 = int(10*uniform())
        list x1

Did each of the digits 0 through 9 occur precisely once?  Did any
not occur?  Which if any occurred precisely twice?  ...more than
twice?  


5. (Continuation) Generate and list a second set of 10 random 
digits, and answer the same questions for it:
        generate x2 = int(10*uniform())
        list x2
How did the answers for x2
differ from the corresponding answers for x1?


6.  Generate an outcome for an event with probability .68 as
follows:  
        Begin a new stata session
        set obs 1
        generate x3 = uniform()
        generate x4 = 0
        replace x4 = 1 if x3 < .68
Did your event occur or not?  Compare notes with classmates.


7.  Repeat #6, without bothering to restart stata, but by
resetting the random number generator:
        set seed xxxxxx   (last 6 digits of your student id)
        set obs 1
        generate x5 = uniform()
        generate x6 = 0
        replace x6 = 1 if x5 < .68
Did your event occur or not?  Compare notes with classmates.


8. After reading Section 4.3 of Moore and McCabe, do the
following exercises beginning on page 322:
	4.39, 4.41, 4.45, 4.47, 4.49


9. After reading Section 4.4 of Moore and McCabe, do the
following exercises beginning on page 340:
	4.51, 4.53, 4.63, 4.71, 4.73