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McGill University, Faculty of Engineering
Course ECSE305A: Probability and Random Signals I
Midterm Examination #1, Fall 2003
Date and time:
Tuesday, October 7, 2003, 14:35  15:55
Examiner:
Prof. B. Champagne
Instructions:
This is a closed book examination: only the faculty standard calculator is
allowed. Attempt all questions.
1.
In a closet, there are 10 pairs of shoes. If six shoes are selected at random, what is the
20 marks
probability of obtaining:
(a)
no complete pair?
(b)
exactly one complete pair?
(c)
exactly two complete pair?
(d)
exactly three complete pairs?
2.
The base (X) and height (Y) of a right triangle are chosen randomly from the intervals
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[0
,b
] and [0
,h
], respectively.
(a)
Deﬁne a suitable probability space for this experiment (specify all three ingredients).
(b)
Find the probability that the area of the triangle so formed will be less than
bh/
4.
3.
Making use of the probability axioms and adequate Venn diagrams (if necessary), prove
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.
 Summer '08
 Bilido

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