After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2’s book, 2 receives 4’s book, 3 receives his or her own book, and 4 receives 1’s book. This outcome can be abbreviated as (2, 4, 3, 1).

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After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2’s book, 2 receives 4’s book, 3 receives his or her own book, and 4 receives 1’s book. This outcome can be abbreviated as (2, 4, 3, 1).

 

 

After all students have left the classroom, a statistics professor notices that four
copies of the text were left under desks. As the beginning of the next lecture,
the professor distributes the four books in a completely random fashion to each
of the four students (1, 2, 3, and 4) who claim to have left books. One possible
outcome is that 1 receives 2's book, 2 receives 4's book, 3 receives his or her
own book, and 4 receives l's book. This outcome can be abbreviated as (2, 4,
3, 1).
a) List all possible outcomes.
b) Let X denote the number of students who receive their own book. Find
the probability mass function for X.
c) Show that X follows a valid probability mass function.
d) Find P(X < 4).
e) Find H. .
f) Find o,.
Transcribed Image Text:After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. As the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2's book, 2 receives 4's book, 3 receives his or her own book, and 4 receives l's book. This outcome can be abbreviated as (2, 4, 3, 1). a) List all possible outcomes. b) Let X denote the number of students who receive their own book. Find the probability mass function for X. c) Show that X follows a valid probability mass function. d) Find P(X < 4). e) Find H. . f) Find o,.
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