What do theta and sigma represent in a Cauchy distribution?
What distribution only has two possible outcomes? (i.e. 1, 0)?
Bernoulli Distribution
Bernoulli Trial PMF:
Bernoulli Trial CDF:
Binomial Distribution PMF:
Binomial Distribution CDF:
Describe a binomial experiment:
A binomial experiment involves a sequence of n (a fixed number) independent and identical
Bernoulli trials with probability of success p (which is constant across trials, as they are
identical).
***Let Y = # of successes from the n trials.*** Then Y is a binomial random variable,
Y ∼ Bin(n, p).
What indicates a large sample in a Binomial distribution?
Geometric Distribution PMF:
Geometric Distribution CDF:
Negative Binomial Distribution PMF:
Negative Binomial CDF:
Distributions based off of Bernoulli trials?
Geometric Distribution
Binomial Distribution
Negative Binomial Distribution
What is the difference between a Binomial distribution and a Negative Binomial distribution?
Binomial: #of successes
Negative Binomial: # of trials until the rth success
In a negative binomial distribution, what happens when r=1?
we get the Geom(p)
Poisson Distribution PMF:
Poisson Distribution CDF:
Hypergeometric Distribution PMF:
Hypergeometric Distribution CDF:
What sort of distribution is this an example of:
Example: Consider Y = the number of 911 calls received in an hour by a phone operator.
Under quite a few assumptions and considering that the average number in an hour is 4.6
Poisson Distribution
What sort of distribution is this an example of:
Example: A shipment of 100 items is examined by testing 3 randomly selected items. Suppose in truth that 8 items are defective.
Hypergeometric Distribution
Formulas related to a Hypergeometric Distribution: