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(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y.
Determine the following:
(a) Do the entries of the table satisfy the conditions for a bivariate density function?
(b) The marginal (or unconditional) probability distributions of X and Y. [Note: These will be a collection of probabilities: the probabilities associated with the 3 values of X and the probabilities associated with the 4 values of Y].
(c) The conditional probability distributions p (X|Y = 3) and p (Y|X = 1). (Note: The first conditional probability distribution is the collection of three numbers, Pr(X = 1jY = 3); Pr(X = 2|Y = 3); Pr(X = 3|Y = 3).)
Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.
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If 28,000 = 85% and 28,000 / X = 100%. What the freak is X and how do you work it out.
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