Today: lab 2 due Monday: Quizz 4 Wed: A3 due Friday: Lab 3 due

Today: lab 2 due • Monday: Quizz 4 • Wed: A3 due • Friday: Lab 3 due • Mon Oct 1: Exam I  this room, 12 pm

Recap last lecture Ch 6.1 • Empirical frequency distributions • Discrete • Continuous • Four forms • F(Q=k), F(Q=k)/n, F(Qqk), F(Qqk)/n • Four uses • Summarization gives clue to process • Summarization useful for comparisons • Used to make statistical decisions • Reliability evaluation

Today Read lecture notes!

Distribution of ages of mothers Sample: students that attended class in 1997 Population: MUN students Unknown distribution

Distribution of ages of mothers Sample: students that attended class in 1997 Population: MUN students Unknown distribution Solution: use theoretical frequency dist to characterize pop Theoretical distribution is a model of a frequency distribution Assumption: observations are distributed in the same way as theoretical dist

Commonly used theoretical dist: Discrete Binomial Multinomial Poisson Negative binomial Hypergeometric Uniform Continuous Normal Chi-square (2) t F Log-normal Gamma Cauchy Weibull Uniform

Theoretical frequency distributions 4 forms

Theoretical frequency distributions - 4 uses • 1. Clue to underlying process • If an empirical dist fits one of the following, this suggests the kind of mechanism that generated the data • Uniform dist • e.g. # of people per table  mechanism: all outcomes have equal prob • Normal dist • e.g. oxygen intake per day  mechanism: several independent factors, no prevailing factor

Theoretical frequency distributions - 4 uses • 1. Clue to underlying process • Poisson dist • e.g. # of deaths by horsekick in the Prussian army, per year  mechanism: rare & random event • Binomial dist • e.g. # of heads/tails on coin toss  mechanism: yes/no outcome

Theoretical frequency distributions - 4 uses 2. Summarize data  dist info contained in parameters e.g. number of events per unit space or time can be summarized as the expected value of a Poisson dist

Theoretical frequency distributions - 4 uses 2. Summarize data e.g. number of events per unit space or time can be summarized as the expected value of a Poisson dist Can make comparisons

Theoretical frequency distributions - 4 uses • 3. Decision making. Use theoretical dist to calculate p-value

Theoretical frequency distributions - 4 uses • 3. Decision making. Use theoretical dist to calculate p-value p(X1qx) p(X2>x)

Theoretical frequency distributions - 4 uses • 3. Decision making. Use theoretical dist to calculate p-value p(X1qx) MiniTab: cdf R: pnorm()

Theoretical frequency distributions - 4 uses • 4. Reliability. Put probability range around outcome

Theoretical frequency distributions - 4 uses • 4. Reliability. Put probability range around outcome MiniTab: invcdf R: qnorm()

Computing probabilities from observed vs theoretical dist

Ch 6.3 Fit of Observed to Theoretical Will present 2 examples: 1 continuous, 1 discrete More examples in lecture notes

Ch 6.3 Fit of Observed to Theoretical Example 1 (Poisson) Number of coal mining disasters, 1851-1866 (England) NDisaster = [4 5 4 1 0 4 3 4 0 6 3 3 4 0 2 4] sum(N)=47 k = [0 1 2 3 4 5 6] = outcomes(N) n = 16 observations

Example 1 (Poisson) Number of coal mining disasters, 1851-1866 (England)

Example 2 (Normal) Age of mothers of students in quant 1997 Are the ages normally distributed?

Example 2 (Normal) Age of mothers of students in quant 1997 Are the ages normally distributed? Strategy  work with probability plots  compute cdf

Example 2 (Normal) Age of mothers of students in quant 1997 Are the ages normally distributed? Strategy  work with probability plots  compute cdf Expected distribution:

Example 2 (Normal) Age of mothers of students in quant 1997 Are the ages normally distributed? Strategy  work with probability plots  compute cdf

Today: lab 2 due Monday: Quizz 4 Wed: A3 due Friday: Lab 3 due