week 6 probability Flashcards
define probability
the likelihood that an outcome occurs between 0 and 1
what is an experiment
process that results in an outcome
what is an outcome
result that we observe
what is a sample space
collection of all possible outcomes of an experiment
what is an event
each possible outcome of the experiment
what is simple probability
described by a single characteristic eg a random day in January
what is a joint probability
described by 2 or more characteristics eg a random day in January that was also a weekday
what is the complement of an event
all events that are not part of that event eg all the days in 2016 that are not january
what is the sum of all probabilities
1
What is marginal probability
the probability of an event irrespective of the outcome of the other joint event
what are mutually exclusive events
events that cannot occur simultaneously eg a day cannot be in January and February
what are collectively exhaustive events
one of the events must occur and the set of events covers the entire sample space
what is conditional probability
probability of one event occuring given that another has already occured
two events are independent if
probability of one event is not affected by the fact that another has ocurred
what does bayes theorem calculate
revises previously calculated probabilities based on new info
bayes theorem formula
P(Bi|A)=
P(A|Bi)P(Bi) / P(A|Bi)P(Bi) + … + P(A|Bn)P(Bn)
what is another name for the expected vallue
mean
why might a weighted average need to be used
some variables are more important than others
when can binomial distribution be used
- two outcomes
- mutually exclusive
- collectively exhaustive
- fixed number of observations
- probabilities are consistent
When can Poisson distribution be used
when you are interested in the number of times an event occurs given an area of oppurtunity
what is an area of opportunity
unit, interval of time,, volume, inwhihc more than one occurrance of an event can occur
In normal distribution mean, median and mode are equal. True or false
true
what is uniform distribution
when smallest value and largest value are equally likely, all values are equally likely
How to shift a normal graph from left to right
Change mean
How to increase or decrease the spread of a normal distribution
change standard deviation
How can we tell a distribution is normal
interquartile range is 1.33std
bell shaped
mean = median
what is standard error of the mean
measure of variability in the mean from sample to sample
does standard error of the mean increase or decrease as sample size increases
decreases
what is considered a large enough sample to be normal
30
what is sampling distribution
distribution of all sample means
what is a confidence interval
a range of values based on observation from one sample
general formula for confidence interval
point estimate +/- (critical value * standard error
)
what is a point estimate
sample statistic of the population parameter of interest
what is the critical valu
based on confidence level eg critical value of a 95% confidence level is 1.96
what is the most important critical value in the world of business
95%
when do we know to use the z value and t value
z value when you know the standard deviation of the population and its mean
if its sample data use t
as the sample size increases, does the t value move closer or further from the z value
closer
what is needed to calculate the ideal sample size to estimate the mean within a certain interval of error
critical value
st dev
acceptable error
how to calculate degree of freedom
size - 1
