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PDB_Stat_100_Lecture_14_Printable

# PDB_Stat_100_Lecture_14_Printable - STA 100 Lecture 14 Paul...

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STA 100 Lecture 14 Paul Baines Department of Statistics University of California, Davis February 4th, 2011

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Admin for the Day I Please pick up Midterm+old homeworks I Important: Homework 3 Solutions posted – please read! I Homework 4 posted, due Wednesday by 5pm! I For Hwk 2 you can get back the points you lost for not printing out and turning in your R output back if. . . You print out your R output, staple it to your graded homework and bring it to me today ! I Project details coming soon. . . References for Today: Rosner, Ch 5.7-5.9, Ch 6.5 (7th Ed.) References for Monday: Rosner, Ch 6.5-6.8 (7th Ed.)
Recap: Continuous Data So far, we’ve talked about tools for three main data types: Type of Data Values it can take Examples Binary Two values Y/N, Male/Female, Ginger/Not, Disease/No Disease, Pregnant/Not ‘Independent 0,1,. . . ,n No. Gingers out of 20 children, Trials’ ( n =no. trials) No. heads out of 10 coin flips, How many injured sloths out of 200 Count 0,1,2. . . No. cases of Lyme disease, (no upper bound) No. traffic accidents No. Vet Emergencies Continuous Any Height (in cm), (Decimals) Blood Pressure, Weight (in lb) Last time we added a fourth. . .

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The Normal Distribution The normal distribution is described by two parameters: 1. The Mean . Denoted by μ . 2. The Standard Deviation . Denoted by σ . 2b. (Equivalently, we sometimes use the variance σ 2 instead) I For continuous data, it can take an infinite number of values and the probability of any taking of specific value is actually zero! I Hence, P ( X 50) = P ( X < 50), P ( X 40) = P ( X > 40). I For the normal distribution it doesn’t matter if we use ‘less than’ or ‘less than or equal to’ (same for greater than). I This still matters a lot for Binomial and Poisson data though! I The area under the curve between two points (a and b, say) is equal to the probability of obtaining a value between a and b .
Useful Rules of Thumb I 68% of the probability falls within μ ± σ I 95% of the probability falls within μ ± 2 σ I 99.7% of the probability falls within μ ± 3 σ I ALWAYS DRAW A PICTURE!!!!!!!! I Put the top of your curve at μ I One SD either side of μ your curve should be just above half the height of the curve at μ I Two SD either side of μ your curve should be about 1/8th of the height of the curve at μ I Shade in the probabilities you are interested in!

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Linear Transformations We can add, subtract, multiply and divide normally distributed random variables rather conveniently. . .

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