I'm working on a problem from Hogg and Tanis, "Probability and Statistical Inference", 8th ed., problem 5.1-7,
$5000 is invested at a rate R selected from a uniform distribution on the interval (.03, .07). Once R is selected the sum is compounded instantaneously for a year so that X=5000e^R by the end of the year.
Find the distribution function of X.
My solution was to say P(X < x) = P(5000e^R<x) = P(R<ln(x/5000)).
This I calculate as the integral from .03 to ln(x/5000) of 10. That come out as 10(ln x/5000-.03) which is not the answer in the back of the book. Help?