3 Random Variables and Discrete Distributions
3.1 Random Variables
Def: A random variable X is a variable whose value depends
on chance, i.e., whose value depends on the outcome of some experiment.
use capital letters to denote random variables
Roll 2 dice, and let X = sum of values on faces.
X is a random variable: its value depends on the outcome of the roll of
the values that X can take are 2, 3, 4, ..., 12.
since this is a discrete set of values, X is called a discrete random
Let R = number of inches of rainfall received at Allentown airport
on given day
R can take on any value in the interval [0, 10] (for example, 3.0", 1.257",
since there is a continuum of possible values, R is called a continuous
Keep flipping a fair coin until you get a tail; let N = number of flips.
N can take on any of the values 1, 2, 3, 4, 5, ...
N is a discrete random variable
A random variable is a function whose domain is the sample space of some
random experiment: the value the random variable takes on is determined
by the outcome of the experiment.
A random variable is discrete if its range (the set of values which it
can take on) is countable, i.e., either finite or countably infinite, and
is continuous otherwise.
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