STAT330 Lecture Notes - Adobe Acrobat, Central Limit Theorem, Histogram

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Christine Dupont

Document Summary

Consider a sequence of i. i. d. random variables x1, x2, . with nite mean e(x) = and. For large n, xn n (cid:16) , 2 n (cid:17). N (0, 1). e. g. consider the distribution of the annual loss of a company as shown below. Density of annual loss y t i s n e. We select a sample of 2 losses and compute the sample mean, x2. We plot the histogram and density (in blue) of the sample means below. Also included is an overlay of the normal density (in red). Density of x2 y t i s n e. Now repeat the same steps: for n = 3: Density of x3 y t i s n e. 0: for n = 15: y t i s n e. 0: for n = 100: y t i s n e. Density of x15 y t i s n e. Density of x100 y t i s n e.