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problem - calculate probability

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  • problem - calculate probability

    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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  • #2
    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 limits-----to 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. --------- -
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    • #3
      hi dear,
      dont get 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.' 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