4.20 & 4.21: Solution | Expectated Value Problems, Exercise of Probability & Statistics by Walpole

In this problem set of 4.20 and 4.21 of chapter four of the 9th edition of"Probability and Statistics for Engineers and Scientists by Walpole", I have solved exercise problems to find the expected value or average value of different random variables which have continuous density functions, and transformed into another domain
4.20 A continuous random variable X has the density function
f(x) = e−x, x greater than 0,
0, elsewhere.
Find the expected value of g(X) = e2X/3.
4.21 What is the dealer’s average profit per automobile if the profit on each automobile is given by g(X) = X2, where X is a random variable having the density function of Exercise 4.12?
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