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COMP 211
DATA AND SYSTEM MODELING (PROB/STAT)
Spring 2012
Assignment #1
Due:
12pm, Wednesday, 2/29/2012
Total points:
200 (each question 10 points)
Please submit a softcopy
(in PDF format
) of your assignment to WebCT before the
deadline. Late penalty: within 24 hours after the deadline:
‐
20%; after 24 hours: 0 point.
Question 1:
Describe a possible sample space for the following experiment: Three chips
are drawn from a lot containing a mix of RAMs (random access memory) and ROM
(readonly memory), and each is checked to see whether it is a ROM or a RAM.
Question 2:
In the experiment described in Question 1, assume that the probability
p(RAM) = ¾ and p(ROM) = ¼ . Compute the probabilities of the following events:
A = At most two RAMs.
B = At least two ROMs.
Are events A and B independent?
Question 3:
The following table shows the outcome of 40 rolls of a die.
Value
Frequency
1
9
2
8
3
5
4
5
5
6
6
7
Find the sample mean and the sample median.
Question 4:
a) Suppose a fair coin is tossed 3 times. Define the sample space Ω.
b) Suppose 3 items are selected from a production process and each item is classified as
either defective or nondefective. Let A be the event that the 1
st
item is defective, B be
the event that there is exactly 1 defective in the 3, and C be the event that all 3 items are
defective.
For each of the following pairs of events, explain whether they are mutually exclusive.
i)
A, B
ii)
A, C
iii)
B, C
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View Full Documentc) Let A be the event that a computer is infected with a virus X. Let B be the event that a
computer is infected with a virus Y. Suppose P(A)=0.15, P(B)=0.05, and P(A
∪
B)=0.17.
Find the probability that
i)
The computer has both virus X and virus Y.
ii)
The computer has neither virus X nor virus Y.
iii)
The computer has virus X but not virus Y.
Question 5:
a) How many ways can 5 people occupy 8 telephone booths if no two people are to
occupy the same booth?
b) A company has hired 15 new employees. 6 of them should be assigned to the day shift,
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 Spring '12
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