Wednesday, January 12
	Topic: Probability and Randomness
	Read: Utts 15
	Read: Utts 16
	Vocab: probability, relative frequency, personal probability, coherent,
	Vocab: mutually exclusive events, independents events, 
	Vocab: cummulative probability, expected value, four probability rules 
	Due: HW #4 @ hw02.shtml

	Review Chi-Squared
	    Hugo -- 5 times in 12 rolls; how unusual is that?
		have students roll 12 dice several times and count number of 
			6's rolled (work in pairs)

	    Berkeley admissions (1=men 2=women) (Utts page 221, exercise 14)
		video clip -- FAPP #10 2:04:45 -- 2:08:40 [didn't show]

		Expected counts are printed below observed counts

		        accept   reject    Total
		    1      450      550     1000
		        416.67   583.33
		
		    2      175      325      500
		        208.33   291.67
		
		Total      625      875     1500
		
		Chi-Sq =  2.667 +  1.905 +
		          5.333 +  3.810 = 13.714
		DF = 1, P-Value = 0.000
		------------------------------------------------	
	Simpson's Parodox
	    If we divide by programs applied to, we see a different story
		------------------------------------------------	
		Expected counts are printed below observed counts
		
		       acceptA  rejectA    Total
		    1      400      250      650
		        403.45   246.55
		
		    2       50       25       75
		         46.55    28.45
		
		Total      450      275      725
		
		Chi-Sq =  0.029 +  0.048 +
		          0.255 +  0.418 = 0.751
		DF = 1, P-Value = 0.386
		------------------------------------------------	
		Expected counts are printed below observed counts
		
		       acceptB  rejectB    Total
		    1       50      300      350
		         79.03   270.97
		
		    2      125      300      425
		         95.97   329.03
		
		Total      175      600      775
		
		Chi-Sq = 10.665 +  3.111 +
		          8.783 +  2.562 = 25.120
		DF = 1, P-Value = 0.000
		------------------------------------------------	
		
	    hospital example (Utts chapter 12, pages 213-215)
		give combined results first, then separate

					survive	die	s rate 	d rate
			standard	  505	 595 	.46	.54
			new		  195	 905	.18	.82
			total		  700	1500	

	
	
			standard 	    5	  95	 .05	.95
			new		  100	 900	 .10	.90
			total		  105	 995	 

	    discrimination example (Utts, chapter 12, pages 215-217) ??

	    death penalty

		326 cases, white defendant: 19/160 get death pen. (.119)
		           black defendant: 17/166 get death pen. (.102)

			when separated by victim's race, see different story
				[overhead from Moore 207]

	    point: statistically significant means that the effect is not 
			likely to be due to chance alone, but there may be
			some other factor than the obvious one that is
			reason

	Probability
	    random: long-term predictability vs short-term unpredictability
		law of large numbers / "law" of small numbers

	    scale: 0 to 1 (0% to 100%)
	    personal vs. mathematical (relative frequency)

	4 Rules and applications
		axiomatic method
	    four rules "overhead"
	    examples
		probability of losing luggage is 1/176 (Krantz)
		
		P(heart attack kills) = .33, P(cancer kills) = .2 
			[assuming death]
		estimated probability of grades
		
		probability of two girls (P(boy) about .512)

		probability of winning 2 of 3, 3 of 5 given an estimate
			for each game
		
	Expected Value
	    lottery example
	    insurance

	video -- Life By the Numbers (#4 Prob) 
		02:00 (or 08:20) - 27:00: intro to prob., Graunt, casinos
		27:00 - 42:25: polling, polio, prob assesses results