assignment1 - COMP 211 DATA AND SYSTEM MODELING (PROB/STAT)...

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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 (read-only 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 non-defective. 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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c) 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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assignment1 - COMP 211 DATA AND SYSTEM MODELING (PROB/STAT)...

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