We returned to the tire molding example (where tires are molded in pairs), and introduced the concept of a probability distribution (a list of possible values the random variable can take and their corresponding probabilities). In this example we calculated the average number of defectives that one may find as a result of 100 runs (where each run produces two tires).
The concept of the expected (mean) value of a random variable X was formalized with a formula and illustrated with a physical analogy, i.e., the centre of gravity. Discussion continued with an important example of home insurance policy where even though the expected profit for the company is positive, it may not be desirable to stay in business if the company insures only a few homes.
We then learned about the variance of a random variable and compared its formula to the formula we used for a population's variance. Three simple examples involving a coin flip were used to illustrate the case of increasing variance and zero variance (loaded coin).
We looked at the important special discrete distribution known as binomial and calculated the probability of getting x successes in n trials. (I illustrated this with three tennis balls and a bucket.) We ended Chapter 4 with an application of binomial distribution to a new drug purchase problem which hospital boards may face.
Since Chapter 4 is now complete, due dates for Assignment 2 are during Week 6, see http://www.business.mcmaster.ca/courses/q600/Assignments/HW2/HW2.html
Chapter 5 is concerned with continuous random variables (such as waiting time, amount of apple juice in a can, or temperature). I illustrated the concept of a continuous random variable with a YouTube video of a bottle filling process. We then looked at the special case of a uniform random variable using the example of the random content of an apple juice can.
The lecture notes for Week 5 (the Thursday section C02) are here.
We will continue with Chapter 5 and finish it during Week 6.
