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If X and Y are random variables, the sum of all the conditional probabilities of X...

If X and Y are random variables, the sum of all the conditional probabilities of X given a specific value of Y will always be: a. 0.0 b. 1.0 c. the average of the possible values of X. d. the average of the possible values of Y.

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Answer #1

The sum of all conditional probabilities of X given a specific value of Y will always be 1.

Option (b) is the correct choice.

For example, say, P(X = a, Y = c) = p, P(X = b, Y = c) = q

X takes only two values a and b.

P(Y = c) = p + q

P(X = a | Y = c) = P(X = a, Y = c) / P(Y = c) =

P(X = b | Y = c) = P(Y = b, Y = c) / P(Y = c) =

Thus, P(X = a | Y = c) + P(X = b | Y = c) = + = 1

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