Module 9.1: Uniform and Binomial Distributions Flashcards
What is a probability distribution?
Describes the probabilities of all the possible outcomes for a random variable. The probabilities of all possible outcomes must sum to 1.
What is a discrete random variable?
The number of possible outcomes can be counted, and for each possible outcome, there is a measurable and positive probability.
What is a probability function?
A probability function, denoted p(x) specifies the probability that a random variable is equal to a specific value.
What are the two properties of a probability function?
1) the probability must be between 0 and 1
2) the sum of all probabilities equals one.
What is a continuous random variable?
The number of possible outcomes is infinite, even if ower and upper bounds exist. The measurement of rain between 0 and 100 inches is a good example, because there is an infinite ways you can measure rainfall.
What are the main differences between a discrete and and continuous probability distributions?
For discrete distribution - the probability is 0 when the event cannot occur. For example, raining 33 days in June.
For continuous distribution - the probability is 0 even though the event can occur.
What is a cumulative distribution function? (CDF)
Defines the probability that a random variable, X, takes on a value equal to or less than specfic value. It represents the sum, or cumulative value, of the probabilities for the outcomes up to and including the specific outcome.
What is a discrete uniform random variable?
A variable for which all the probabilities for all possible outcome for a discrete random variable are equal.
What is a binomial random variable?
What is a Bernoulli random variable?
Defined as the number of “Successes” in a given number of trials, whereby the outcome can be either “success” or “failure”.
Bernoulli random variable - A binomial random variable for which the number of trials is 1.
What is the formula for Binomial probability?
p(x) = n! / (n-x)!x! * p^x * (1-P)^(n-x)
x = # of successes - example: "you draw 3 beans" n = # of trails - example: ""you will draw 5 beans from the bowl" p= probability of selecting a bean on any given attempt
What is the formula for variance of a binomial random variable?
variance of X = np(1-p)
n = number of days, trials p = probability of event - example: "probability of success"
What is a continuous uniform distribution?
Defined over a range that spans between some lower limit a, and some upper limit b, which serve as the parameters of the distribution.
What are the properties of a continuous uniform distribution?
1) All outcomes are between the upper and lower bound
2) probability outside the boundaries is 0
3) the probability between two numbers is the difference of those numbers divided by the upper and lower boundary.
