Summary: Version: 03/20/2003
H. Ayhan, J. G. Dai, R. D. Foley
Due: MWF sections on Friday, 28th of March, TTh sections on Thursday 27th of March.
1. Suppose we are producing wire which is extruded as a long, continuous strand. After each 100
meters, the wire is cut and placed on a spool. Defects in the wire appear at random and on
the average there are 10 defects per kilometer of wire. For notation, let N(t) be the number
of defects in the first t meters of wire produced, S0 = 0, Sn be the location of the nth defect,
Tn be the time between the (n - 1)st and nth defect, and be the rate of defects per meter
(a) What is the rate of defects per meter of wire?
(b) What is the expected number of defects in the first spool?
(c) What is the mean number of defects in the tenth spool?
(d) What is the probability that the first spool contains no defects?
(e) What is the probability that the tenth spool contains one defect?
(f) What is the probability that the tenth spool contains one defect given that the first nine
spools contained no defects?
(g) What is the probability that there is exactly one defect among the first ten spools?
(h) What is the average location of the first defect?