Supplementary Exercise 4.78 of IPS7e
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Independence or dependence between random variables in specific settings.


(a) Two rainfall amounts at the same location one year apart. Because the
weather has mostly short-term dependence, one could reasonably assume
these measurements to be independent. They will both reflect the
expected weather patterns in November at the particular location, and
if compared with totally different weather situations (e.g. in the
summer), some similarity would be expected. This is however not what we
would usually consider as statistical dependence.


(b) Two rainfall amounts on successive days at the same location. As stated above,
weather has mostly short-term dependence, and therefore rainfall amounts
on two succesive days will show some dependence. Obviously rainfall
amounts one hour apart at the same location will show stronger
dependence, but the dependence one day apart may still be appreciable
(that may depend on local weather patterns).


(c) Two rainfall amounts on nearby locations at the same day. These should
show even stronger dependence than discussed above for (b). The same
weather system could produce rain at both locations.