Suppose one has a stereo system consisting of two main parts, a radio and
a speaker. If the lifetime of the radio is exponential distribution with mean
1000 hours and the lifetime of the speaker is exponential distribution with
mean 500 hours independent of the radio’s lifetime, then what is the
probability that the systems failure (when it occurs) will be caused by the
radio failing? (15%)
The service times for customers coming through a checkout counter in a
retail store are independent random variables with a mean of 1.5 minutes
and a variance of 1.0. Find the probability that 100 customer can be
serviced in less than 3 hours of total service time. (15%)
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