SOC 885 Study Guide - Final Guide: Pivotal Quantity, Confidence Interval, Exponential Distribution

• School: Ryerson University
• Department: Sociology
• Course: SOC 885
• Professor: Abednego Aryee

Document Summary

Refer to example 8. 4 and suppose that y is a single observation from an exponential distribution with mean . a use the method of moment-generating functions to show that 2y/ is a pivotal quantity and has a. Use the pivotal quantity 2y/ to derive a 90% confidence interval for . c compare the interval you obtained in part (b) with the interval obtained in example 8. 4. Example 8. 4 suppose that we are to obtain a single observation y from an exponential distribution with mean . Use y to form a confidence interval for with confidence coefficient . 90. Suppose that is a single observation from an exponential distribution with mean. Step-2: since is a single observation from an exponential distribution with mean. The above moment generating function is similar to the moment generating function for a distribution with 2 df. Because it is free, it is a pivotal quantity.