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class01-2-handouts

# class01-2-handouts - PSTAT 120B Probability Statistics...

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PSTAT 120B - Probability & Statistics Class # 01-2 - Functions of random variables Jarad Niemi University of California, Santa Barbara 31 March 2010 Jarad Niemi (UCSB) Functions of random variables 31 March 2010 1 / 18

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Class overview Announcements Announcements Office hours: Jarad Niemi: MWF 11am-noon and 2-3pm Varvara Kulikova: W 3-5pm @ 5431S Qunying Shen: M 12-2pm @ 5431A GauchoSpace: Check regularly. Post homework questions here rather than emailing. You are responsible for content on GauchoSpace. Homework Due 4pm on Mondays (but can be turned in at class) Homework 1 is posted and is due 5 April 2010 by 4pm Some points will be awarded for attempting all problems and a subset of the problems will be graded for content. Jarad Niemi (UCSB) Functions of random variables 31 March 2010 2 / 18
Class overview PSTAT 120B Goals PSTAT 120B Goals If we observe Y 1 , Y 2 , . . . , Y n iid f Y ( y | θ ), What is a reasonable value for θ ? What is a procedure we can use to get a value? What do we mean by reasonable? How reasonable are the values returned by these procedures? What is a reasonable range for θ ? What is a procedure we can use to get a range? What doe we mean by reasonable? How reasonable are the ranges returned by these procedures? What if we want to compare hypotheses about the possible values for θ ? How can we formally compare these hypotheses? Everything we do in this course will work toward some reasonable ways of answering these questions. Jarad Niemi (UCSB) Functions of random variables 31 March 2010 3 / 18

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Class overview Day’s Goals Goals Consider a random variable Y with a known distribution, what is the distribution of U = f ( Y ) for some function f ( · )? Method of Distribution Functions Method of Transformations Method of Moment-Generating Functions (Friday) Jarad Niemi (UCSB) Functions of random variables 31 March 2010 4 / 18
Class overview Why?

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