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.
[40 pts] 4. Consider a signal detector to detect if a signal is present or not, as shown below:
EECS 126
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