PDB_Stat_100_Lecture_09_Printable

# PDB_Stat_100_Lecture_09_Printable - STA 100 Lecture 9 Paul...

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Unformatted text preview: STA 100 Lecture 9 Paul Baines Department of Statistics University of California, Davis January 24th, 2011 Admin for the Day I Homework 1 can be picked up today (in class or outside my office) I Midterm: Wednesday, Jan 26th, in class I No R or R Commander knowledge needed for this midterm I Closed book – one double-sided page of notes + calculator I Extra office hours: Mon 9.30-11.30am, Tues 10.00-11.00am References for Today: Rosner, Ch 4.1-4.12 (7th Ed.) References for Wednesday: Everything so far (Midterm) Topics for Today 1. Probability for discrete data 1.1 Genetics Example 1.2 Binomial Distribution 1.3 Probability Mass Functions 1.4 Random Variables 1.5 Mean and Variance 1.6 Computing Binomial Probabilities Recap: Useful Rules Recall: AND = ∩ , OR = ∪ , GIVEN = | . Rule/Definition Formula Mutually Exclusive: P ( A or B ) = P ( A ) + P ( B ) Exhaustive: P ( A or B ) = 1 Addition Rule: P ( A or B ) = P ( A ) + P ( B )- P ( A and B ) Complement: P ( A c ) = 1- P ( A ) Independence: P ( A and B ) = P ( A ) × P ( B ) General AND: P ( A and B ) = P ( A ) × P ( B | A ) Bayes Rule: P ( B | A ) = P ( A ∩ B ) P ( A ) = P ( B ) P ( A | B ) P ( B ) P ( A | B )+ P ( B c ) P ( A | B c ) Brief Recap A couple of common things that have come up: I Rule of thumb: SD ≈ Range/5 I Right-Skew: Mean > Median, Median closer to lower quartile I Left-Skew: Mean < Median, Median closer to upper quartile I Symmetric: Mean ≈ Median, Median half way between lower, upper quartiles I 0th-Percentile is the minimum value (by convention) I 100th-Percentile is the maximum value I IQR = Upper Quartile - Lower Quartile I Outlying values: LQ - 1.5*IQR, UQ + 1.5*IQR Types of Data Remember the different types of data? Q: All the probability we have seen so far has been suitable for what type of data? A: Discrete data – mainly binary and ‘ k out of n ’ data. Examples: disease/no disease, guilty/not guilty, heads/tails, dice rolls, # of ginger children out of n . Today we add some more types of data to that list: ‘count’ data. Genetics Recap Q: With two ( R , r ) parents, each child has a 1 / 4 probability of being a ginger. If the parents have 2 children what is the probability that they will both be gingers? A: Requires first child AND second child to be ginger: P ( 1st child is ginger ∩ 2nd child is ginger ) = = P ( 1st child is ginger ) x P ( 2nd child is ginger ) [the above requires independence] = 1 4 x 1 4 = 1 / 16 ....
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## This note was uploaded on 01/17/2012 for the course STAT 100 taught by Professor drake during the Fall '10 term at UC Davis.

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PDB_Stat_100_Lecture_09_Printable - STA 100 Lecture 9 Paul...

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