Ch 3 Random Variable & Probability Dist.

probability

the chance that one event will happen

long-run probability

probability proves true in the long run (doing event many times)

ordinary random variation

small differences are very likely to occur simply due to chance

any probability value is btwn…

0 & 1

sum of the probabilities is equal to…

1

complement rule (not A)

P(A^C ) = 1- P(A)

addition rule

P(A or B) = P(A) + P(B)

when can you use the addition rule?

when A & B have no common events. mutually exclusive/disjointed

the general addition rule

P(A or B) = P(A) + P(B) - P(A n B)

when can you use the general addition rule?

if A & B are common events. not mutually exclusive/not disjointed

conditional probability

given that B has occurred, find the probability that A has occurred

conditional probablility calculation

P (A | B) = P(A n B) / P(B)

independent events

unrelated

P(A n B) if events are independent

P(A) x P(B)

P(A | B) if events are independent

P(A) * P(B) / P(B)

how do you test for independence?

if P(A | B) = P(A)P

probability of at least one

1- P(none)

empirical rule is AKA…

68-95-99.7 rule

empirical rule

68% of data found within 1SD of mean

95% of data found within 2SDs of mean

99.7% of data found within 3SDs of mean

when can you use the empirical rule?

when you have a normal dist.

given a value of data in a normal dist., how can you find the proportion of data less than that value in R?

pnorm(x, mean, SD)

given a value of data in a normal dist., how can you find the proportion of data greater than that value in R?

1-pnorm(x, mean, SD)

what does pnorm tell you in R?

the proportion of data less than that value

given a percentile or top/smallest proportion of data in a normal dist., how can you find what value it corresponds to in R?

qnorm(0.95, mean, SD)

(0.95 is an ex., use any proportion)

how do you calculate IQR of a normal dist. using R?

qnorm(0.75, mean, SD) - qnorm(0.25, mean, SD)

how would you find ex. the middle 95% or data in a normal dist.?

subtract 97.5 - 2.5