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Joint Distributions -Two or More RVs
•
So far we discussed only a single RV
•
In real (useful) experiments, we usually collect information on two or
more quantities simultaneously
•
Pressure, Volume, Temperature
•
Service Times, # of A/C units
•
# of cars and # of trucks on a Hwy
•
fuel consumption and average speed traveled
•
height and weight
•
time until failure of two different components
•
We need to be familiar with probabilistic modeling of two or more RV’s
•
Prediction of one variable given the values of the other(s)
Section 5.1
Joint Distribution for Discrete RV’s
Def: The joint pmf of
X
and
Y
is a function
p
(
x
,
y
) or
p
XY
(
x
,
y
)
satisfying:
Genuine joint pmf:
Let A be a set of (x,y) pairs. Find the P(A):
e.g. A = {(x,y): x + y = 5} or A = {(x,y): x
≥
3, y
≤
4}

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Example 5.1
X = auto policy deductible
Y = homeowner’s policy deductible
...for a randomly selected person in an insurance pool
Joint Probability Table
Marginal Distributions
The
marginal
pmf’s
of X and Y, denoted by p
X
(x) and p
Y
(y) are