Answer to Question #15611 in Statistics and Probability for abid khan
2012-10-01T08:03:55-04:00
Conditional Probabilities:Select all of the following statements that are true for all joint distributions over X and Y
P(x,y)=P(x)P(y)
P(x,y)=P(x|y)P(y)
P(x,y)=P(x|y)P(y|x)
P(x)=∑yP(x|y)
P(x)=∑yP(x,y)
None of the above.
1
2012-10-02T10:34:13-0400
Only statement (2) and (5) are true in general. (1) By definition holds if X and Y are independent (2) P(x,y)=P(x|y)P(y) this is definition of P(x|y): P(x|y) = P(x,y)/P(y) (3) the expression P(x|y)P(y|x) has no sense (5) ∑yP(x,y) means the sum over all y of values P(x,y). This sum is equal to P(x) (4) ∑yP(x|y) means the sum over all y of P(x|y)=P(x,y)/P(y): ∑yP(x|y) = ∑y P(x,y)/P(y) again this sum has no sense (6) None of the above. This is also not true, since (2) and (5) are correct
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