Module 2 Flashcards
what is probability
random process generates outcome A equals the proportion of times the outcome would occur across a very larger number of independent repetitions of the process
PROBABILITY IS LONG-TERM RELATIVE FREQUENCY
probability is estimated by observing many many occurrences.
Frequentist definition of probability
Probability Rules
- The probability of an outcome must be a number between 1 and 0
- All possible outcomes together must have a total probability equal to 1
- Probability of A + Probability of B must = 1 - Complement Rule - probability that an even does NOT occur equals 1 minus the probability that the event does occur.
- Addition Rule
- if events A and B are mutually exclusive if they have no outcomes in common and can never occur simultaneously
If not mutually excludive
PrAandB = PrA + PrB - Pr(AandB) - Multiplication Rule
- if A and B are indepdendent
PrAandB = PrA x PrB
Independent if knowing that one occurs does not give information about the probability of the other - not mutually exclusive because its possible for both to occur simultaneously - separate events two dice
Complement Rule -
probability that an even does NOT occur equals 1 minus the probability that the event does occur.
Addition Rule
- if events A and B are mutually exclusive if they have no outcomes in common and can never occur simultaneously
If not mutually excludive
PrAandB = PrA + PrB - Pr(AandB)
Multiplication Rule
- if A and B are indepdendent
PrAandB = PrA x PrB
Independent if knowing that one occurs does not give information about the probability of the other - not mutually exclusive because its possible for both to occur simultaneously
- separate events two dice would be independent
Tversky and Kahneman
Likelihood of feminist movement, bank teller, bank teller and feminist movement
Multiplication rule makes it so bank teller and feminist movement is less likely because of multiplication rule
relative frequency is __________ to probability
eqivalent
The probability of randomly selecting a score that is exactly equal to 3 is ________ because on a continuous scale of infinite values ___________
0 bc the value of 3 is a single point and points have a width of 0 because on a continuous scale of an infinite number of values, the value of 3 is a signle point and points have a width of 0
thus with continuous distributions, non-zero probabilities exist only for an interval of possible observations.
Probability density function
describes the population probability distribution of a random variable
the probability of any outcome or event is ___________
the area under the curve bounded by the values that define the event
The total area under the curve defined by a probably density function always equals
1
Probability rule 2
For a continuous variable X, the probability of observing a value between a and b equals the area under the curve defined by the probability density function of X that falls between point a and b which is found via _______
integration
Normal distribution or curve is also called
normal probability density function
u =
population mean
population mean symbol
u