Ch. 5 Proximity in Our Daily Lives

Explain what long/short-run proportion provides us with

LONG-RUN PROPORTION

* gives basis for definition of probability
* gets closer/closer to certain number
* get rid of uncertainty/randomness
* \

SHORT RUN PROPORTION

* highly random/variable

\

\*\* as # of trials increases = proportion of times # becomes predictable/less random

What is the law of large number

* Jacob Bernoulli proves # of trials increases….proportion of occurances approaches certain number in LONGRUN
* he assumes outcome of any trial does NOT depend on outcome of other trials

Define probability

PROBABILITY

* randomized experiment/sample/stimulation, probability is the proportion of times the outcome occurs in a Long Run of observations
* takes a value of 0→1 (decimal/fraction not %)

What are independent trials

INDEPENDENT TRIALS

* dif. trials of a random phenomenon are indpendent if outcome of any trials is not affected by the outcome of another trial

How do we find probability

FINDING PROBABILITY

* make assumptions about nature of random phenomenon
* ex: symmetry→assume that possible outcomes are equally likely (dice/coin)

What are some types of probability

TYPES OF PROBABILITY

* __**subjective**__
* rely on sub. info bc you do/can NOT have any
* probability of outcome is **personal** (ur degree of belief that outcome occurs based on available info)
* __**objective**__
* use data from long-run trials

List the rules of probability

**unconditional**___

\
SAMPLE SPACE

* list of individual outcomes of random phenomenon
* btwn 0→1
* sum = 1


* ==Probability== ==of event== is sum of prob of indiv. outcomes from sample space making up event
* P(A) = # of outcomes of A / # of outcome in sample space
* For event ==A compliment== (does NOT occur)
* P (A^c) = 1 - P(A)
* ==UNION== is 2 events (A or B or both)
* P (A or B) = P(A) + P(B) - P(A&B)
* ==INDEPENDENT== /intersection of 2 events
* one doesn’t affect the other
* P(A&B) = P(A) \* P(B)
* ==DISJOINT/MUTUALLY EXLUSIVE==
* when A and B have no common elements
* one event affects the other
* P(A&B) = 0

What unconditional vs. conditional

UNCONDITIONAL= no special conditions assumes other than ones in experiment

\
CONDITIONAL = prob. reflects additional knowledge

* assumes what event B is, reduces the sample space
* P(A|B) = P(A&B) / P(B)

What are sensitivity or specificity

Sensitivity P(S) = probability of state (present

* prevalence

\
Specificity P(S^c) = truly negative rate (not present)

List Bayes’ Rule

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