# Lec09 - Ch 4: Learning Objectives 4: Learning Objectives...

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I E/Stat 265, Fall 2009 O /Stat 65, a 009 Lecture #9: ontinuous Distributions Co uous s bu o s Ch 4-1 4-4 1 h 4: Learning Objectives Ch 4: Learning Objectives etermine probabilities from PDF CDF ± Determine probabilities from PDF, CDF. ± Determine PDF from CDF and vice-versa alculate Means Variances for continuous ± Calculate Means, Variances for continuous distributions and functions of one variable ± Understand assumptions for 7+ common CDFs p ± Standardization of Normal random variable ± Use Tables for Standard Normal ± Use approximations for Binomial and Poisson distributions. 2 oday’sTop ics Today s Topics 4-1 Probability Density Functions 4-2 Cumulative Distribution Functions and Expected Values 3 Continuous Random Variables 4-1 Continuous Random Variables ± Definition: A r.v. X is said to be continuous if its set of possible values is an entire interval of real numbers. ± Example: suppose X is an rv representing all values for a dowel diameter between 15 and 20 m. mm. X would be defined simply as 15 X 20 4 Could X = an imaginary number?

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ontinuous Vs Discrete Continuous Vs. Discrete ± Key issue: if units for X can be subdivided to any extent Æ continuous; if not Æ discrete ± Money – ? ± Height – ? ± Practical Uses – lthough many continuous variables have limitations in the precision ± Although many continuous variables have limitations in the precision to which they may be measured (e.g. precision of measuring instrument), we still treat them as continuous. ± Similarly, some discrete variables also may be treated as continuous. 5 ± Why? Æ continuous variables are generally easier to manipulate. robability Density Functions Probability Density Functions ± Probability Density Function scales the frequencies / counts so that they integrate to 1. rovide a continuous scale for X ± Provide a continuous scale for X. Mapping With Greater Precision 6 X 0M 0 M “nearest mm” Probability Density Function (PDF) 4-1. Probability Density Function (PDF) apping a continuous rv X as a “density” defines a ± Mapping a continuous rv X as a density , defines a probability density function as an f(x) that satisfying
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## This note was uploaded on 03/17/2010 for the course IOE 265 taught by Professor Garyherrin during the Fall '09 term at University of Michigan-Dearborn.

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Lec09 - Ch 4: Learning Objectives 4: Learning Objectives...

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