After all students have left the classroom, a statistics professor notices that four copies of th text were left under desks the beginning of the next lecture, t professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim 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). (a) List the other 23 possible outcomes. (1234) (1 243) (1342) (1 324) (1432) (1 423) (2143) (2134) (2341) (2314) (2431)(2x (b) Let X denote the number of students who receive their own book. Determine the pmf of X. (Enter your answers as fractions.) 1 0 3 X p(x) 0.375 0.333 0.25 0 0.041666 x

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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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).
(a) List the other 23 possible outcomes.
(1 2 3 4) (1 2 4 3) (1 3 4 2) (1 3 2 4) (1 4 3 2) (1 4 2 3) (2 1 4 3) (2 1 3 4) (2 3 4 1) (2 314) (2431) (2 ×
(b) Let X denote the number of students who receive their own book. Determine the pmf of X. (Enter your answers as fractions.)
0
1
2
3
4
X
p(x)
0.375
✓
0.333
0.25
0
0.041666
X
Transcribed Image Text: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). (a) List the other 23 possible outcomes. (1 2 3 4) (1 2 4 3) (1 3 4 2) (1 3 2 4) (1 4 3 2) (1 4 2 3) (2 1 4 3) (2 1 3 4) (2 3 4 1) (2 314) (2431) (2 × (b) Let X denote the number of students who receive their own book. Determine the pmf of X. (Enter your answers as fractions.) 0 1 2 3 4 X p(x) 0.375 ✓ 0.333 0.25 0 0.041666 X
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