Cumulative Distribution Functions and Expected Values : Solved Example #1

These questions are taken from the book 'Probability and Statistics for Engineering and the Sciences' by Jay L. Devore (8th Edition)

Question : Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is CDF of X

Use the cdf to obtain the following:

a) P X is less than or equal to 1
b) P .5 is less than or equal to X is less than or equal to 1
c) P X is more than 1.5
d) The median checkout duration Median
e) F’x to obtain the density function f(x)
f) E(x)
g) VX and Standard Deviation of X.
h) If the borrower is charged an amount hX = X­­2 when checkout duration is X, compute the expected charge EhX.

0:00 Introduction to Cumulative Distribution Functions and Expected Values : Solved Example #1
0:14 Introduction to Question
0:26 Part (a)
1:34 Part (b)
3:00 Part (c)
3:59 Part (d)
5:45 Part (e)
7:15 Part (f)
8:41 Part (g)
11:02 Part (h)

[mrak]

Why it was not x^2/4 dxin integration?