chapter 12: Introducing Probability Flashcards
The sample space S of a random phenomenon
the set of all possible outcomes.
An event
an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space S.
A probability model
a mathematical description of a random phenomenon consisting of two parts: a sample space S and a way of assigning probabilities to events
Benford’s Law
A random variable
a variable whose value is a numerical outcome of a random phenomenon.
The probability distribution of a random variable X
tells us what values X can take and how to assign probabilities to those values
A finite random variable
has a finite list of possible outcomes
if all outcomes in a sample space are equally likely, we find the probability of any event by…
Time is a ________ variable.
continuous
disjoint
when two events have no outcomes in common and so can never occur together
Simulations are used for
random outcomes where the underlying probability is known.
Y
the outcome of random variables
continuous probability models
assign probabilities as areas under a density curve. The area under the curve and between any range of values is the probability of an outcome in that range.
Z
a standard(ized) normal variable
randomness
individual outcomes are uncertain but happen in a predictable manner through time
The probability of a particular outcome is the __________ of times the outcome would happen in a very long series of repetitions.
proportion
For any continuous random variable X, P(X = a) equals ____ for all values a.
0, because it’s got no area in the density curve, because it’s just one value, i.e. sliver
area of a triangle
(width x height)/2
To figure out the number of unique ways to choose r things out of n total things
n!
the product of all whole numbers from 1 to n
