6. After all students have left the classroom, a statistics professor notices th

Question

6. After all students have left the classroom, a statistics professor notices that three copies of the textbook were left behind in class. At the beginning of the next lecture, the professor distributes the three books back in random order to the three students (1, 2 and 3). One possible outcome is (3, 2,1), which means student 1 receives the book belonging to 3, student 2 receives her own book back and student 3 receives the book belonging to 1. (a) List all six ways in which the books can be distributed back to the students. (b) Let X denote the number of students who get their own books back. For outcome (3,2, 1), for example, 1 student gets their own book back. Write down the pmf and the cdf of X.

Explanation / Answer

a) SIx ways

1 2 3 No. of students who get the book back = X=3

1 3 2 X=1

2 1 3 X=1

2 3 1 X=0

3 1 2 X=0

3 2 1 X=1

For X= 0 Probability =2/6

X=1, Probability = 3/6

X=2 , Probability=1/6

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