i want to ask that when we have to calculate probability ,where a bivariate fuction is given ,then under what conditions do we integrate first w.r.t x and then w.r.t y(i.e first fix y and integrate w.r.t x and then we integrate w.r.t y) and under what conditions we integrate first w.r.t y and then w.r.t x(i.e first fix x and integrate w.r.t y and then integrate w.r.t x)?(e.g there is a question ..f(x,y)=x+y and we have to calculate P(2x<1/x+y<1),here we integrate 1st w.r.t x and then w.r.t y i.e dxdy BUT in another question where f(x,y)=2x+y we have to calculate P(x+y<0.5) and in this question we integrate 1st w.r.t y and then w.r.t x i.e dydx,,,in both cases 0<x<1,0<y<1..i do have solutions for both questions)plz answer the conditions for the both cases
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problem  calculate probability
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you folks are confusing me you need to look at the formula of bivariate variables it says f(x,y)=integral, integral f(x,y) dy dx  if you want to do dx first and dy second then you must change the limitsto change the limits you have to draw a diagram which is much more difficult if you still want to do that way dx 1st dy 2nd than check your calculus book the section that cover calculus III in statistics exam it's standard dy dx you must solve for dy to get to dx. 

hi dear,
dont get confused....it has a very simple logic....
if we have given joint pdf and we need to calculate marginal one thn we use the abv....for ex we are given joint pdf of x and y two r.v.'s....as f(x,y). and we want to know marginal pdf of x i.e. f(x) or of y i.e. f(y), then we simply integrate the joint pdf f(x,y) with y and x respectively.....
limits will get change accordingly....
i hope now u have got it....P FM MFE MLC C
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