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# Random Thoughts 2012 (COMP 066) PowerPoint PPT Presentation

Random Thoughts 2012 (COMP 066). Jan-Michael Frahm Jared Heinly. Assignment. Calculate the probability of being pregnant with a positive pregnancy test for a women with age 27 and for a women of age 44 in 2008. Use the Bayes rule to compute the probability.

Random Thoughts 2012 (COMP 066)

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## Random Thoughts 2012(COMP 066)

Jan-Michael Frahm

Jared Heinly

### Assignment

• Calculate the probability of being pregnant with a positive pregnancy test for a women with age 27 and for a women of age 44 in 2008. Use the Bayes rule to compute the probability.

• Read in the Moldinov book chapter 6.

• Bayes rule

### Bayes Rule for Pregnancy Test

Age 27: [99.99%, 84.16%]

Age 44: [ 99.96%, 37.67%]

### Spam filtering

• Often done based on black list

• too restrictive

• easy to evade by putting false sender e-mail

• Bayes rule can be used to perform spam filtering

• Filtering based on words in the e-mail

• “viagra” has high probability of spam

• “Bayes-rule” has low probability of spam

• can be learned from e-mails

### Probability Rules

• Probability of event = p

• ex. probability of rolling a 1 on a die: p = 1/6

• Probability of event not happening = 1 – p

• ex. probability of not rolling a 1: p = 5/6

• Probability of event happening n times in a row = pn

• ex. probability of rolling five 1s in a row: p = (1/6)5

• Probability of event happening at least once during n attempts = Inverse of probability of event not happening n times in a row = 1 – (1 – p)n

• ex. probability of rolling a 1 at least once in 5 rolls: p = 1 – (5/6)5

### Probability Rules

• Probability of event happening k times in n attempts

• Binomial

• Can only add probabilities when you want to know if any one of a set of outcomes occurred and it is impossible for the outcomes to occur at the same time

• ex. probability of rolling a 1 or a 2 on a die: p = 2/6

### Expected Value

Σ

• Expected value = probability of event * value of event

• Ex: pay \$1 to play a game, 10% chance of winning \$5, 40% chance of winning \$1

• Expected Value = -1 + 0.1 * 5 + 0.4 * 1 = \$-0.10

### Perceptual Pitfalls

• The probability that two events will occur can never be greater than the probability that each will occur individually.

• “a good story is often less probable than a less satisfying … [explanation]”

• Missing information

• Availability bias

• recallable prior knowledge influences our estimates

### Odds vs. Probability

• Odds vs Probability

### Binomial distribution

• Binomial distribution: For events with K successes in N trials

• Properties of a Binomial distribution:

• Fixed number of trials

• Only outcomes are success and fail?

• Same probability for success in each trial

• Independent trials (no influence of previous trials to current trial)

### Description of Data

• Mean

• Average

• Median

• Middle value

• Standard deviation

• Variability or spread of the data

• Percentile

• Position within ordered list of values

### Confidence Interval

• Margin of error of N samples

z*=

Number of samples needed:

### How many trials?

• Margin of error for a population proportion

• Depends on proportion in the population that had the characteristic we searched for