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Committee - Probability and Random Processes - Exam, Exams of Probability and Statistics

Bharat Ratna Dr. B. R. Ambedkar UniversityProbability and Statistics

Main points of this exam paper are: Committee, Picked Randomly, Committee, Men, Probability, Heads, Coin and Flip

Typology: Exams

2012/2013

Uploaded on 04/01/2013

raheem
raheem 🇮🇳

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EECS 126
EECS 126 -- MIDTERM # 1 Professor Ren
October 9 , 1997, Thursday 6-8 p.m.
[15 pts.] 2. A committee of four is picked randomly from a pool of 5 men and 4 women. Find the
probability that there will be more women than men on the committee.
[25 pts ] 3. Given two coins with probability of heads being p1 for coin 1, and p2 for coin 2. You
randomly pick a coin and flip it.
Let: X = the number of heads in n flippings of the randomly picked coin.
Y = the number of flippings it takes to get the first head (flipping the randomly picked coin).
a) Find the probability mass functions of X and Y, respectively.
b) Suppose you flipped k times already and still have not got a head yet. Find the probability that you
picked coin 1.
file:///C|/Documents%20and%20Settings/Jason%20Raft...%20-%20Fall%201997%20-%20Ren%20-%20Midterm%201.htm (1 of 2)1/27/2007 4:25:15 PM
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EECS 126

EECS 126 -- MIDTERM # 1 Professor Ren October 9 , 1997, Thursday 6-8 p.m.

[15 pts.] 2. A committee of four is picked randomly from a pool of 5 men and 4 women. Find theprobability that there will be more women than men on the committee.

[25 pts ] 3. Given two coins with probability of heads being p1 for coin 1, and p2 for coin 2. Yourandomly pick a coin and flip it.

Let: X = the number of heads in n flippings of the randomly picked coin. Y = the number of flippings it takes to get the first head (flipping the randomly picked coin).

a) Find the probability mass functions of X and Y, respectively.

picked coin 1.b) Suppose you flipped k times already and still have not got a head yet. Find the probability that you file:///C|/Documents%20and%20Settings/Jason%20Raft...%20-%20Fall%201997%20-%20Ren%20-%20Midterm%201.htm (1 of 2)1/27/2007 4:25:15 PM

EECS 126

[40 pts] 4. Consider a signal detector to detect if a signal is present or not, as shown below:

where X is the received signal plus noise, and

not present (with probability 1/2)X = {^ S , when the signal is present ( with probability 1/2)^ |^ M , when the signal is S is a uniform random variable in [-,2], and M is a Gaussian RV with distribution N(0,1).

a) Find the pdf of X. b) Let g(X) = | X - 1|. Find the pdf of Y = | X - 1|. c) Given that Y >= 1, find the probability that the signal is present.

file:///C|/Documents%20and%20Settings/Jason%20Raft...%20-%20Fall%201997%20-%20Ren%20-%20Midterm%201.htm (2 of 2)1/27/2007 4:25:15 PM