Statistics Chapter 6 Flashcards
What is a random variable? (2)
A variable whose value depends on the outcome of a random event
The outcome is not known until the experiment is carried out
What is a random variable’s sample space?
The range of values it can take
What is a discrete variable?
A variable that can only take certain numerical values
What does a probability distribution do?
It fully describes the probability of any outcome in the sample space
What is a probability mass function?
A way of describing the probability of any outcome in the sample space
e.g. P(X=x) = 1/6, x = 1, 2, 3, 4, 5, 6
What is a discrete uniform distribution?
A distribution where all probabilities are the same
For a random variable X, ΣP(X = x) = ?
1 for all x
When can X be modelled with a binomial distribution, B(n,p)? (4)
Fixed number of trials, n
Two possible outcomes (success or failure)
Fixed probability of success, p
Trials are independent of each other
If a random variable X has binomial distribution, B(n,p) what is its probability mass function?
P(X=r) = (n r) p^r (1-p)^(n-r)
Cumulative Probabilities - greater than n
Means - X > n
Calculation - 1 - P(X < n)
Cumulative Probabilities - no more than n
Means - X < n
Calculation - P(X < n)
Cumulative Probabilities - at least n
Means - X >/ n
Calculation - 1 - P(X < [n-1] )
Cumulative Probabilities - fewer than n
Means - X < n
Calculation - P(X < [n-1] )
Cumulative Probabilities - at most n
Means - X < n
Calculation - P(X < n)
