Statistics - Statistical Distributions Flashcards
What is a random variable?
A variable whose value depends on the outcome of a random event. A variable is random if the outcome is not known until the experiment is carried out.
What is a sample space?
The range of values that a random variable can take is called its sample space.
What is a discrete variable?
A variable is discrete if it can only take certain numerical values.
What is a probability distribution?
A probability distribution fully describes the probability of any outcome in the sample space.
What is a discrete uniform distribution?
When all the probabilities are the same.
What is the random variable X equation?
The sum of the probabilities of all outcomes of an event add up to 1. For a random variable X, you can write P(X=x) = 1 for all x.
Under what conditions can you model X with a binomial distribution, B(n,p)?
- if there are a fixed number of trials, n
- if there are two possible outcomes (success and failure)
- if there is a fixed probability of success, p
- if the trials are independent of each other
If P(Success) = p and there are only two possible outcomes, then P(Failure) = 1 - p.
If a random variable X has a binomial distribution B(n,p), what is its probability mass function given by?
X ~ B(n,p)
P(X = r) = (n | r)p^r (1-p)^n-r
What is the index?
n is sometimes called the index
What is the parameter?
p is sometimes called the parameter
What does a cumulative probability function for a random variable X tell you?
A cumulative probability function for a random variable X tells you the sum of all the individual probabilities up to and including the given value of x in the calculator P(X< or equal to x)
What is a continuity correction?
- The normal approximation to the binomial distribution can be improved by adding a continuity correction.
- The continuity correction accounts for extra data from the same class width that has been cut off by the limits of the probabilities we want to find.
