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mba 522 discrete RV - integer or not

# mba 522 discrete RV - integer or not - Again we start with...

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Values of Discrete RVs Need Not be Integer Students often confuse/equate countability of a discrete RV with it being "integer" in value! Discrete variables are those whose outcomes are COUNTABLE from a finite or infinite series, but the values do not necessarily have to be integer (although they often are!). Here are examples: Finite series A salesman makes 50 calls in one day. The number of actual sales is discrete and will take on the values: 0, 1, 2, 3, ....... , 50. We must include zero b/c none of the 50 calls could be successful, and we go up to 50 as the upper value because the total calls made were 50. So, the maximum sales made would be 50. Infinite Series Number of people who apply for a tourist visa to the U.S. in a year. Here the number is countable, but there is no upper limit on it. The values would be: 0, 1, 2, 3, .........
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Unformatted text preview: Again, we start with zero b/c nobody might apply for a visa -- although this is highly unlikely and its f(x) will be zero. But we can't put an upper limit on it b/c we don't know the total number of people who may apply in one year. Please note that although in majority of cases a discrete RV has integer values, but that is not a requirement. See the following example: Discrete, non-integer RV XYZ Bank in Lincoln, NE offers mortgage loans. The interest rates offered by the bank in the month of September are: 6.5%, 7.0%, 8.2%. Let's say 100 people apply for loans in September and you record the data: 30 get the 6.5%, 50 get the 7%, and 20 get the 8.2%. X f(X) 0.065 0.3 0.07 0.5 0.082 0.2 1.0 You can see in this case, the random variable, X, which is interest rates is not integer. But it is countable. Dr. J....
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