Chapter 2 (Random Variables without 2.6) Flashcards
What does a random variable do?
It assigns a numerical value to each outcome of an experiment.
What is a discrete random variable?
A random variable that has a countable number of outcomes.
ie between any two outcomes there is a gap. Countable does not necessarily mean finite!
What is a continuous random variable?
It takes on values defined by an interval or intervals. The outcomes cannot be counted.
(I.e. If the outcomes are measurements, they can also be measured more precisely.)
What is the distribution of a random variable?
The set of all possible values of the random variable and their associated probabilities
What is a probability mass function (pmf)? How do we display it?
The way we describe the distribution of a discrete random variable.
Usually done with a table but can be done in a graph.
X______|___________
P(X=x)_|___________
The rules for the pmf are…
The same rules for normal probability.
0 ≤ P(A) ≤ 1, where A is an event.
P(Ω) = 1, or all the events added together = 1.
What is the cumulative distribution function of a discrete random variable? (cdf)
The cdf of the discrete random variable X is a function of the form F(x) = P(X ≤ x)
__x____|________
P(X=LTx)_|_______
What does pmf short for?
When is it used?
probability mass function.
Used for discrete random variables.
What is cdf short for?
What does it do?
cumulative distribution function.
Sums up the probabilities of random variables ≤ a specified value.
What is the expected value of a random variable X?
How is it denoted?
E(X). It is the mean of the distribution of X.
What is the variance of a random variable X?
How is it denoted?
Var(X). It measures the variability in the values taken on by the random variable.
What formula can we use to find Var(X)?
Var(X) = E(X^2) - [E(X)]^2
Also denoted sigma^2.
What is the standard deviation of a random variable X? How is it denoted?
It is the positive square root of the variance, and is therefore denoted with sigma.
What is a probability density function (pdf)?
How do we display it?
the distribution of a continuous random variable.
It is usually displayed in function notation.
What is pdf short for?
Probability density function
