Suppose classes in your major’s department come in three categories: “open to all”, “majorsonly”, and “directed studies”. Also, suppose that the following make reliable models for thenumber of students in a class, X:• For a class that is open to all, the number of students X is Poisson distributed with anaverage of 400.• For a class that is majors-only, the number of students X is Binomial distributed withparameters n = 50 and p = 1/4.• For a class that is directed studies, the number of students X is Binomial distributedwith parameters n = 4 and p = 1/2.Suppose you just need to take one more class from your major’s department this fall.Out of all the classes you COULD take, there are 5 classes in your major’s department thatare open to all, 8 classes that are majors only, and 2 classes that are directed studies. Youcan’t decide which to take, so you choose one at random, with each class equally likely tobe picked.Use the above information to calculate the following:(a) The conditional expectation of X given the chosen class is open to all.(b) The conditional expectation of X given the chosen class is majors only.(c) The conditional expectation of X given the chosen class is directed studies.(d) The expected value of X.Note: Do NOT include yourself in your answers!
Suppose classes in your major’s department come in three categories: “open to all”, “majors
only”, and “directed studies”. Also, suppose that the following make reliable models for the
number of students in a class, X:
• For a class that is open to all, the number of students X is Poisson distributed with an
average of 400.
• For a class that is majors-only, the number of students X is Binomial distributed with
parameters n = 50 and p = 1/4.
• For a class that is directed studies, the number of students X is Binomial distributed
with parameters n = 4 and p = 1/2.
Suppose you just need to take one more class from your major’s department this fall.
Out of all the classes you COULD take, there are 5 classes in your major’s department that
are open to all, 8 classes that are majors only, and 2 classes that are directed studies. You
can’t decide which to take, so you choose one at random, with each class equally likely to
be picked.
Use the above information to calculate the following:
(a) The conditional expectation of X given the chosen class is open to all.
(b) The conditional expectation of X given the chosen class is majors only.
(c) The conditional expectation of X given the chosen class is directed studies.
(d) The
Note: Do NOT include yourself in your answers!
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