IEOR 165 Lecture 2 May 27 2009

# IEOR 165 Lecture 2 May 27 2009 - Lecture Notes IEOR 165 |...

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry Homework due Tuesday Statistic always talks about a population. Example: Population x random variable of interest (but we can have more than just one) Probability theory: = : μ Ex mean or also called the mathematical expectation of x = = - σ2 Varx Ex2 Ex2 = . Fxx Px x is probability distribution function PDFof x Fx fully characterizes . . the r v of x = fxx ddxFxx Derivative of PDF = pdf (probability density function) The Probability distribution function gives us a lot of information. But for instance, in a test, When x is a discrete random variable, = { = } fxx P x x probability mass function (pmf) If we have a homogenous population, we know that it will be a normal distribution ( ) fx x Students % % at each score If (e.g.), X is normally distributed, then = * - - , -∞< <∞ fxx 12π σexp 12x μσ2 x Now back to our example: Population x random variable of interest (but we can have more than just one) Task: Estimate the mean and variance of the population x. Sampling (Random samples) x1, …, xn (of size n) Since this is a random sample, then we know that E[ xk ] = E[x] = μ and Var( xk ) = Var(x) = σ2 Estimate the population mean μ (we can find this easily, but we’re doing better by finding the BEST estimate) A possible estimator of

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## This note was uploaded on 07/22/2009 for the course IEOR 165 taught by Professor Shanthikumar during the Summer '08 term at University of California, Berkeley.

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IEOR 165 Lecture 2 May 27 2009 - Lecture Notes IEOR 165 |...

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