Lecture 4: Random Variables and Distributions - University of Washington
Lecture 4: Random
Variables and Distributions
Goals
? Random Variables
? Overview of discrete and continuous
distributions important in genetics/genomics
? Working with distributions in R
!
Random Variables
A rv is any rule (i.e., function) that associates
a number with each outcome in the sample
space
-1
"
0
1
Two Types of Random Variables
? A discrete random variable has a
countable number of possible values
? A continuous random variable takes all
values in an interval of numbers
!
Probability Distributions of RVs
Discrete
Let X be a discrete rv. Then the probability mass function (pmf), f(x),
of X is:
f (x) =
P(X = x), x
x?
0,
A
Continuous
a
Let X be a continuous rv. Then the probability density function (pdf) of
X is a function f(x) such that for any two numbers a and b with a b:
b
P(a " X " b) =
#
a
f (x)dx
a
b
................
................
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