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

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 4 (chap4) Donghyung Lee
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Note Read sections 4.1-4.6 Summary note for probability theory, set theory, counting will be posted on our course website this week.
Background image of page 2
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 - = =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Section 4.2 The Normal Curves Normal Distribution (3) (from wikipedia.org)
Background image of page 6
Section 4.2
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 22

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online