BiVariate Worksheet

# BiVariate Worksheet - Random Variables Independence: Two...

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Random Variables Independence: Two random variables, X and Y, are said to be independent if P(X and Y) = P(X) P(Y) . for all possible values of X and Y. Example: Consider the experiment of tossing a coin two times. A convenient sample space is {HH, HT, TH, TT}. Let X denote the number of heads on the first toss and Y the number of heads on the second toss. Then the joint distribution of X and Y is given by: y 01 x 0 .25 .25 1 .25 .25 Are X and Y independent? To determine this, compute the marginal probabilities P(x) and P(y). Each is given by P(0) = 1/2, P(1) = 1/2. Entering this in the table we have: y 0 1 P(x) x 0 .25 .25 .5 1 .25 .25 .5 P(y) .5 .5 1.0 Hence for all cells in the joint probability distribution, the probability is equal to the product of the marginals. This means that X and Y are independent as expected. What does independence tell us? Essentially, that knowledge of the value of one random variable tells us nothing about the value of the second random variable, or that the two variables vary separately.

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Problems: 7.3.a Given the bivariate probability distribution: y 123 x 1 .2
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## This note was uploaded on 01/03/2011 for the course COMM 290 taught by Professor Brian during the Winter '09 term at UBC.

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BiVariate Worksheet - Random Variables Independence: Two...

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