Hi! That is a good question. If you are asked to find the distribution of a function of two random variables, then you need an auxiliary variable for the other transformation. If your primary transformation is U=X/Y, then choose V=Y (denominator). If the primary is U=XY (or V=X+Y), then choose V=X (or V=Y). If U=log(XY)=log(X)+log(Y), then V=log(X) or V=log(Y) may be a good choice. Each problem is different. The keys are 1) make sure that U and V are 1-to-1 functions of X and/or Y and 2) to make the variable V as simple as possible. If you cannot easily determine the auxiliary variable, sometimes you may have to use trial and error (last resort). I hope this helps!- Mark
Keep going 😎
More video about hypothesis ,sampling distribution
See the Playlist for Mathematical Statistics :-)
Thankyou
How do we choose a good auxilary variable??
Hi! That is a good question. If you are asked to find the distribution of a function of two random variables, then you need an auxiliary variable for the other transformation. If your primary transformation is U=X/Y, then choose V=Y (denominator). If the primary is U=XY (or V=X+Y), then choose V=X (or V=Y). If U=log(XY)=log(X)+log(Y), then V=log(X) or V=log(Y) may be a good choice. Each problem is different. The keys are 1) make sure that U and V are 1-to-1 functions of X and/or Y and 2) to make the variable V as simple as possible. If you cannot easily determine the auxiliary variable, sometimes you may have to use trial and error (last resort). I hope this helps!- Mark
Its a thumps up! 😊