18.44 Lecture Notes - Lecture 21: Random Variable, Unit Circle, Standard Deviation
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Answer: note that y 27 if and only if x 3. Hence p{y 27} = p{x 3}= f (3). Suppose p{x a} = f (a) is known for all a. Generally f (a) = p{y a} = p{x a }=f (a ) If x is a continuous random variable and g is a strictly increasing function of x and. Y = g(x) ,then f (a) = f (g (a)) In other words, the probability mass functions for x and y are the row and columns sums of ai,j. If x and y assume values in {1,2,,n} then we can view a = p{x = i, y = j} as the entries of an n n matrix. Let"s say i don"t care about y . I just want to know p{x = i}. Given the joint distribution of x and y , we sometimes call distribution of x (ignoring y ) and distribution of y (ignoring x) the marginal distributions.
