Lecture 4

# Lecture 4 - Probability and Statistics in the Life...

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Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 4 (chap4) Donghyung Lee

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Note Read sections 4.1-4.6 Summary note for probability theory, set theory, counting will be posted on our course website this week.
Section 4.2 (supplement) Probability Density Function Probability Density Function (pdf) : Let X be a continuous random variable. If a nonnegative function f satisfies followings, then it is called the probability density function (pdf) of X: (1) ( ) 0 (2) ( ) 1 (3) ( ) ( ) b a f x for all x f x dx P a X b f x dx e - = =

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Section 4.2 The Normal Curves Normal Distribution (1) : A continuous random variable X is said to follow a normal distribution with mean and standard deviation , where and , if the probability density function of X is ( denotes the base of the natural logarithm and equals approximately 2.718 and approximately equal to 3.14 ) μ σ - 7 < < 0 < 2 2 ( ) /(2 ) 1 ( ) , 2 x f x e x πσ - - = - < < I π e 2 ~ ( , ) X Normal μ σ
Section 4.2 The Normal Curves Normal Distribution (2) 1. A continuous distribution with single peak, that is unbounded and symmetric about the mean ( which is equal to the median and mode). 2. The normal distribution is the most important one in all of probability and statistics. 3. Many numerical populations have distributions that can be fit very closely by an appropriate normal curve. (ex) heights, weights, measurement errors in scientific experiments, reaction times in psychological experiments, scores on various tests

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Section 4.2 The Normal Curves Normal Distribution (3) (from wikipedia.org)
Section 4.2

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## This note was uploaded on 03/28/2011 for the course AMS 110 taught by Professor N/a during the Spring '08 term at SUNY Stony Brook.

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Lecture 4 - Probability and Statistics in the Life...

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