Joint Probability and Statistics
A joint probability distribution of a group of random variables is the distribution of group of
variables as a whole. Applied business statistics deal mostly with the joint probability
distribution of two discrete random variables. The joint probability distribution of two discrete
random variables is the likelihood of observing all combinations of the two variables.
Joint Probability Function:
Let us have two discrete random variables X and Y, taking values
x
i
, i = 1,.
...,m, and y
i
, j = 1,.
....,n, respectively. The function:
P
X, Y
= P
X, Y
(x, y) = P(X = x, Y = y)
is called the joint probability function of the random variables X and Y.
As an example, consider two competitive stocks (A, and B). Suppose the estimated rates of
return of stocks A and B are given as follow (respectively):
R
A
= [0.8, 1.0, 1.2], and R
B
= [0.9, 1.0, 1.1]
The numbers in the body of the following table are the estimated probabilities of all possible
combinations of two jointly probabilities of the two random variables R
A
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 Spring '08
 Staff
 Probability distribution, Probability theory, Rb, Joint probability distribution, Marginal distribution

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