Calculus 2, Lec 12B, PDFs & CDFs, Simulate a Normal Distribution, Areas and Volumes by Slicing

Calculus 2, Lecture 12B.

(0:00) We will look at applications of pdf's and cdf's in actuarial science.
(0:39) Review of content from Lecture 12A.
(3:39) Review the standard normal curve on Mathematica in the context of pdf's and cdf's (do simulated sampling from the distribution).
(11:31) Areas and Volumes by slicing, starting with the area between two curves.
(13:21) Discussion of taking an intuitive approach rather than a rigorous approach and derivation of the formula for the area between two curves.
(20:59) Volume of an arbitrary three-dimensional solid by slicing.
(25:48) Example: Volume of a solid whose cross-sections above a triangular region are squares.