| Stat 250 Fall 1998 |
Name ________________________________ |
| Activity #6: Binomial distribution |
Student ID __ __ __ - __ __ - __ __ __ __ |
|
Section # 1
2 |
Form a group of 3-4 students. You will be given 15 minutes
to complete this activity.
Recall that a binary categorical variable is a variable that
has two possible outcomes. For example, gender (male/female), having
a tattoo (yes/no), and education status (student/non-student) are all examples
of binary categorical variables.
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As a group, be creative in thinking of a binary categorical variable which
would be "measured" on people. Define the variable and identify the
two possible traits. Arbitrarily choose two letters of the alphabet
to represent the two possible traits. (If I were not creative,
and chose gender as my binary variable, then the two possible traits would
be male and female. I'd arbitrarily label being male an M and being
female an F.)
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Now, suppose you randomly select three people. You plan to "measure"
the people with respect to your binary categorical variable. Using
your notation defined above, list the 8 possible outcomes that could occur.
(For my example, all three people could be male, i.e. MMM, or the first
person could be male and the second and third persons could both be female,
i.e. MFF, and so on. With three people, there are 8 possible such
outcomes.)
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Arbitrarily, pick one of the two possible traits for your original variable
you defined in #1. (I'd pick, say, being male, M.) Then,
for each of the 8 outcomes you listed in #2, identify how many times
the trait you picked could occur. (For my example, for MMM, there
are 3 males, but for MFF, there is 1 male.)
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Assume that each person has a probability of 0.8 of having the trait that
you picked in #3. (So, I'd assume that the probability of male
is 0.8. A little unrealistic, but just the same.) Then,
assuming independence, calculate the probability that if you randomly select
three people, none of them will have your trait of interest. (I'd
calculate the probability of getting three females, i.e. the probability
of getting FFF.)
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Using the same assumptions as in #4, what is the probability that if you
randomly select three people, that one of them will have your trait of
interest?
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Using the same assumptions as in #4, what is the probability that if you
randomly select three people, that two of them will have your trait of
interest?
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Try to identify a pattern in your calculations in #4, #5, and #6.