I distributed a Handout on continuous distributions, containing a list of essential formulas for continuous random variables.
I continued with examples of problems involving continuous distribution. In the first problem, the "half life" of a radioactive substance (i.e., the time until half of the substance had decayed) was given, and one had to determine the length of time it took for 90 percent of the substance to decay, assuming that the decay time is exponentially distributed. The second problem illustrated the "maximum trick": Given n random numbers in the interval [0,1], find the density of the largest of these numbers. The last problem served as an illustration of how to compute the density of a function of a given random variable: Given that X has standard normal distribution, find the density of Y=eX,
Additional problems of this type are contained in this week's homework assignment.