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Random Thoughts 2012 (COMP 066)

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Random Thoughts 2012(COMP 066)

Jan-Michael Frahm

Jared Heinly

- 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

Age 27: [99.99%, 84.16%]

Age 44: [ 99.96%, 37.67%]

- 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 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 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

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

- 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

- 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)

- Mean
- Average

- Median
- Middle value

- Standard deviation
- Variability or spread of the data

- Percentile
- Position within ordered list of values

- Margin of error of N samples

z*=

Number of samples needed:

- Margin of error for a population proportion
- Depends on proportion in the population that had the characteristic we searched for