Question

In: Statistics and Probability

For each case, indicate whether the count response would be better model with Poisson or a...

For each case, indicate whether the count response would be better model with Poisson or a binomial distribution

(a) You randomly visit 12 married couples who have been married for 20 years and count the number that have no children.

(b) You visit 12 married couples with children, and count the number of times in the past year that each family has had visited the hospital emergency room.

(c) During an hour of studying, you count the number of times you get a text.

(d) During an hour of studying, you count the number texts that you decide to reply to.

(e) Suppose you arrive at the bus loop every Monday morning at 9:00 for 14 consecutive weeks. You count the number of buses each week that fill up before you get on one.

(f) Suppose you arrive at the bus loop every Monday morning at 9:00 for 14 consecutive weeks. You count the number of times your friend is in line ahead of you when you arrive.

(g) For a full term, you count the number of typos on a particular professor’s slides in each lecture.

(h) For a full term, you count the number of midterms that have at least one typo on them.

(i) Professor counts the number of students who are asleep at the mid-point of a particular lecture.

Solutions

Expert Solution

Solution:

For binomial distribution the number of trials should be finite, whereas for poisson distribution the number of trials is not finite.

a) The number of trials is 12, which is finite, therefore for the given scenario the count response would be better model with binomial distribution.

b) The number of trials is 12, which is finite, therefore for the given scenario the count response would be better model with binomial distribution.

c)  The number of points within an hour is not finite which results in infinite number of trials, therefore for the given scenario the count response would be better model with poisson distribution.

d) The number of points within an hour is not finite which results in infinite number of trials, therefore for the given scenario the count response would be better model with poisson distribution.

e) The number of trials is 14, which is finite, therefore for the given scenario the count response would be better model with binomial distribution.

f) The number of trials is 14, which is finite, therefore for the given scenario the count response would be better model with binomial distribution.

orchestra answered 1 year ago
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