Supplementary Exercise 4.14 of IPS7e
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Choices of sample space for different settings.

(a) The study time cannot go beyond the interval (0,24) hours. In
practice, values close to 24 hours seem very unlikely, but as they are
not impossible, the most natural sample space is S=(0,24).


(b) We are counting the number of physicians out of 11,000 who had a
heart attack in a five-year period. It will be an integer number in the
range 0,...,11000. Both of the endpoints appear quite unlikely, but as
they are not impossible the most natural sample space is
S=(0,1,2,...,11000).


(c) The number of broken eggs is an integer number between 0 and 12.
Therefore, S=(0,1,2,...,12).


(d) Dollar amounts are strictly speaking discrete (because we cannot get
values inbetween the lowest-value coins), but it may be a good approximation
to say consider the cash amount as continuous in a suitable interval. The lower
interval limit should be zero but it is not obvious what to choose for the upper
bound. One possibility is to choose an unbounded upper interval limit (that is,
infinity), but of course it is possible to set a realistic upper bound for how 
much cash any person is carrying. We could for example use S=(0,100000)
dollars; no person is ever going to carry more than 100,000 dollars!


(e) Weight gains are measured on a continuous scale, apart from
measurement round-off. Both positive and negative values are possible,
but it is not obvious what the lower and upper bounds should be.
If we for example say that rats never exceed 5 kgs in weight (presumably
very sensible), we could use S=(-5000,5000) g. 


Note: In several of these examples, the sample space could be chosen narrower 
if desired, but in practice there is no gain in doing so. If we use a normal 
distribution to describe a continuous outcome (e.g., the weight gains),
the corresponding sample space will be unbounded, from minus infinity to 
infinity. Also for counts we sometimes use distributions with an
unbounded sample space, such as the Poisson distribution for non-
negative counts, i.e. S=(0,1,2,3,...).