This week is short due to fall break. We have two days to cover 6.7, and begin 8.1: ------------------------------------------------------------------ Wed: 6.7 probability * first, a few minutes on discussing activity on 6.4 * lecture - follow book pretty carefully. Main ideas: . prob. dens. functs f(x) satisfy (1) f(x) >= 0 (2) integral from -inf to +inf is 1. . example 2 in book, expontential distribution (describes waiting times and equipent failure) . mean is Mu = integral of xf(x), maybe explain why, and maybe find the mean of the exp. dist. . median is m s.t. integral from m to inf of f(x) is 1/2 . example = normal distributions, draw for various sigma(=std. dev) This is alot to get through. But the HW problems are nice (I suggest 1, 2*, 4, 6*, 10*) ------------------------------------------------------------- R/F: begin 8.1: sequences - should get through 1. intro. to seq, 2. a_n = f(n) same limit 3. limit laws (sum properties, etc). Spend whole hour on Activity: Slightly modified version of Harel's discovery based intro. to sequences. (next week do comparison test, and bounded monotone seq, ex. recursively defined seq. and induction) --------------------------------------------------------------