random phenomena
everyday situations from which the outcome is uncertain
phenomena
any observable occurences
long run proportion
the proportion of times an event occurs over a very large number of trials, essentially defining the probability of the event
trial
each occurrence
cumulative proportion
the number of occurrences of a specific result/ the amount of trials over time
the law of large numbers
as the number of trials in a random experiment increases, the average of the results will get closer and closer to the expected value
independent
the outcome of any one trial is not affected by the outcome of any other trial
relative frequency
the probability of an outcome as a long-run proportion
subjective definition of probability
the probability of an outcome is defined to be a personal probability- your degree of belief that an outcome will occur, based on available information
sample space
the set of possible outcomes
- tree diagrams
- multiply the # of possible outcomes on each trial by each other
event
a subset of the outcomes/ sample space
the probability of each individual outcome is
between 0 and 1
the sum of probabilities of the individual outcomes in a sample space is
equal to 1
the complement of an event
for an event A, all outcomes of the sample space that are not in A are the complement of A
denoted by A^c
disjoint
two events that do not have any common outcomes
intersection
consists of outcomes that are both in A and B
union
consists of outcomes that are in A or B or both
conditional probability
deals with finding the probability of an event when you know that the outcome was in some particular part of the sample space
random variable
a numerical measurement of the outcome of a random phenomenon
mean of the probability distribution
the expected value of x
condition for the binomial distribution
- each trial has the same probability of a success
- n trials are independent
- each n trial has two possible outcomes
Some useful rules for finding probabilities associated with normally distributed z scores:
i) P(z is above some value) = 1 - P(z is below that value)
ii) P(z is more than/beyond a certain +- value) i.e. in either direction = P(z is below the - value) + P(z is above the + value) Equivalently 2P(z is below the - value)
–> because the normal distribution is symmetric on each side of the mean
iii) P(z within/ between a certain +- value) = 1 - P(z is more than/beyond that +- value)
iv) P(z within/ between any particular upper and lower values) = P(z is below the upper value) - P(z is below the lower value)
