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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