Conditioning multiple random variables on events. Let X
Chapter , Problem 27(choose chapter or problem)
Conditioning multiple random variables on events. Let X and Y be continuous random variables with joint PDF fx.y , let A be a subset of the two-dimensional plane, and let C = {(X, Y) E A}. Assume that P(C) > 0, and define { fx.Y (x, y) fx.Ylc (x, y) = P(C) , 0, (a) Show that fX.Ylc is a legitimate joint PDF. if (x, y) E A, otherwise. (b) Consider a partition of the two-dimensional plane into disjoint subsets Ai , i = 1, ... , n, let Ci = {(X. Y) E Ad, and assume that P(Ci ) > 0 for all i. Derive the following version of the total probability theorem n fx,y (x, y) = L P(C)fX.YICi (x, y) . i=1
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer