Downloadable - About University

94 Introduction to probability
(a) Calculate the expected number of requests received and interpret
your results.
(b) Is this a discrete or a continuous probability distribution?
(13) You are thinking of selling your house and you reckon that there is
a 0.1 probability that you will sell it for $120 000, a 0.5 probability
that you will receive $100 000 for it and a 0.4 probability that you
will only receive $80 000. What is the expected selling price of the
property? Interpret your result.
(14) A toll bridge over the River Jay is operated by a private company
who are thinking of installing automatic machines to collect the
tolls. These machines, however, are not perfectly reliable and it is
thought that the number of breakdowns occurring per day would
follow the probability distribution shown below:
Number of breakdowns per day
0 1
Probability 0.4 0.6
When a breakdown occurred, revenue from tolls would be lost
until the equipment was repaired. Given below are approximate
probability distributions for the equipment repair time and the
average revenue lost per hour.
Equipment
repair time Probability
Average revenue
lost per hour Probability
1 hour 0.7 $40 0.6
2 hours 0.3 $50 0.3
$60 0.1
(a) Determine the probability distribution of revenue which would
be lost per day as a result of machine breakdowns (it can be
assumed that the above probability distributions are independent).
(b) Calculate the expected loss of revenue per day and interpret
your result.
Reference
1. Moore, P. G. and Thomas, H. (1988) The Anatomy of Decisions (2nd edn),
Penguin, Harmondsworth.