This quiz is for giving you a feel for the type of skills
and inclination you need to take this course. You should be able to solve these
problems, or at least want to solve such problems.
1) A server system has 3 components. The probability that a component is busy is p. What is the probability that a request is rejected, assuming - (i) the request needs all 3 components together for execution; (ii) the request needs any one out of the 3 components (iii) the request needs any 2 out of 3 components for execution. (Possible answers for (i),(ii),(iii) are listed in that order).
a)
1 – (1-p)3, p3, p3+3p(1-p)2
b)
3p, p, 2p
c)
p3,
1 - p3, 6p
d) 1 – (1-p)3, p3, p3+3p2(1-p)
2) A network transmits three kinds of messages: E-mail, Web and FTP. 50 % of the messages are e-mail, 40% are WWW transfers and 10% are FTP. E-mail message sizes (in KB) have geometric distribution with parameter 0.04, Web message sizes have geometric distribution with parameter 0.02 and FTP messages have geometric distribution with parameter 0.005. Given that a message of size 100 KB has arrived for transmission, what is the probability that it came from a Web application?
a) (0.0299 ´ 0.98 ´ 0.4) / (0.0299 ´0.98 ´ 0.4 + 0.0499 ´ 0.96 ´ 0.5 + 0.00599 ´ 0.995 ´ 0.1)
b) (0.9899 ´ 0.02 ´ 0.4) / (0.9899 ´0 .02 ´ 0.4 + 0.9699 ´ 0.04 ´ 0.5 + 0.99599 ´ 0.005 ´ 0.1)
c) 0.4
d) 0.4 ´0.02100
3) Let X and Y be discrete random variables with Uniform distribution over the set {1,2,3,…n}. If W=X+Y, what is the value k at which Pr[W=k] is the highest?
a) All values; W also has a uniform distribution.
b) n
c) 2n
d) n+1
4) Consider the program segment shown. Assume that Prob(B=true) = p, Prob(B1 = true) = 3/5 and Prob(B2 = true) = 2/5. Exactly one statement is common to statement groups S1 and S2: write (“good day”). After many repeated executions of the program segment, it has been estimated that the probability of printing exactly three “good day” messages is 3/25. Derive the value of p.
if B then
repeat S1 until B1
else repeat S2 until B2