STAT 3470 Study Guide - Midterm Guide: Random Variable, Maximum Likelihood Estimation, Exponential Distribution

• School: Ohio State University
• Department: Statistics
• Course: STAT 3470
• Professor: All

Document Summary

Please show all work to receive full credit for each problem. Please indicate if and when you use a calculator, making sure to write out the steps. P (x > 8) = 1 p (x 8) = 1 (1 e 8/6) = e 8/6 0. 2636 (b) (4 points) let x1, x2, , xn be a random sample from this distribution. What are the expected value and variance of the sample average wait time x = 1 i=1 xi? npn (both versions the same) we know. 36 n (c) (5 points) now suppose n = 35. What is the (approximate) probability that the average of these 35 wait times is between 3 and 6 (6 and 9) minutes? (version a) P (3 < x < 6) = p (cid:18) 3 6. P ( 2. 96 < z < 0) = p (z < 0) p (z < 2. 96) = 0. 5000 0. 0015 = 0. 4985, where z n (0, 1). (version b)