4.13 & 4.14: Solution | Expectated Value Problems, Exercise of Probability & Statistics by Walpole

In this problem set of 4.13 and 4.14 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.
4.13: The density function of the continuous random variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year, is given in Exercise 3.7 on page 92 as
f(x) =
⎧ x, 0 x 1,
⎨2 − x, 1 x 2,
⎩0, elsewhere.
Find the average number of hours per year that families run their vacuum cleaners.
4.14: Find the proportion X of individuals who can be expected to respond to a certain mail-order solicitation if X has the density function
f(x) = 2(x+2)/5 , 0 x 1,
0, elsewhere.
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