Problem Set 1
September 14, 2009
Due date:
Monday, September 28 2009 at 4pm; before class.
Exercise 1:
(20 points) Some years ago, greek videoclub chain
Seven
had the following offer to their
customers:
every time a customer rented a DVD, he was given a random coupon with the title of the
Academy awards (Oscars) winner movie written on it. The first person to gather the coupons with all the
unique winnermovie titles won a 10day vacation on a Carribean island.
If at that time, there were 75
unique such titles, and these titles were uniformly assigned to coupons, find the
expected
number of DVDs
one had to rent in order to gather all of them. (Nocredit question: when was the competition held?).
Exercise 2:
(20 points) Assume an array of
n
numbers
X
=
{
x
1
, ..., x
n
}
.
Write the pseudocode of an
algorithm that computes the mean and the variance of the numbers by making a single pass over the data
and using
O
(1) storage space. Recall that given
X
, the
mean
of X is given by
x
=
1
n
n
i
=1
x
i
,
and the variance of
X
is given by
var
(
X
) =
1
n
n
i
=1
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 Fall '09
 Variance, Data Mining, Probability theory, Natural number, serial episode

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