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hw-1-solution - CSE 221 Probabilistic Analysis of Computer...

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CSE 221: Probabilistic Analysis of Computer Systems Spring 2008 Swapna S. Gokhale Homework #1 Solutions Date: Feb. 15, 2008 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. The sample space is given by: s0 = (RAM, RAM, RAM) s1 = (RAM, RAM, ROM) s2 = (RAM, ROM, RAM) s3 = (RAM, ROM, ROM) s4 = (ROM, RAM, RAM) s5 = (ROM, RAM, ROM) s6 = (ROM, ROM, RAM) s7 = (ROM, ROM, ROM) 2. In the experiment described in Problem #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? The probabilities of the sample points are as follows: p(s0) = ¾ x ¾ x ¾= 27/64 p(s1) = ¾ x ¾ x ¼ = 9/64 p(s2) = ¾ x ¼ x ¾ = 9/64 p(s3) = ¾ x ¼ x ¼ = 3/64 p(s4) = ¼ x ¾ x ¾ = 9/64 p(s5) = ¼ x ¾ x ¼ = 3/64 p(s6) = ¼ x ¼ x ¾ = 3/64 p(s7) = ¼ x ¼ x ¼ = 1/64 A = at most two RAMs (0, 1, or 2 RAMs) p(A) = p(s1) + p(s2) +…+ p(s7) = 37/64
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