The sugar company will choose from two companies to transport its sugar to market. The first company charges 5197 to rent trucks
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a) has CDF
where the last equality follows from independence of . In terms of the distribution and density functions of
, this is
Then the density is obtained by differentiating with respect to ,
b) can be computed in the same way; it has CDF
Differentiating gives the associated PDF,
Assuming and
, we have
and
I wouldn't worry about evaluating this integral any further unless you know about the Bessel functions.