Joint PDF - May 21

[Amit Goyal]

May21_Joint_PDF.png

[SHIKHA]

case 1:u<0
F(U,V)=0

case 2: v<0
F(U,V)=0

case3: u>=1 v>=1
 F(U,V)=1
 case 4: 0<=u<1 v>=1
F(U,V)=u^3+u^2-u^5

case 5: u>=1 0<=v<1
F(U,V)=1-u^5

case 6:0<=u<1  0<=v<1
F(U,V) =0 if v<=u
F(U,V)= (v^2-u^2)(v^3-u^3) otherwise

[anon_econ]

Umm. Sir, can we or can we not say that P(U<u,V<v)=P(X>Y).P(Y<u,X<v)+P(Y>X).P(X<u,Y<v)?

[SHIKHA]

sir atleast tell if my answer is correct or nt??

[Amit Goyal]

Shikha,

Let me give you the density and then you can check your answer by integrating it.

Correct answer:
Joint Probability Density function of U = min{X, Y} and V = max{X, Y} is
h(u, v) = 6uv(u + v) for 0 < u ≤ v < 1, zero, elsewhere

And Vasudha, you can write this:
P(U<u,V<v)=P(X>Y).P(Y<u,X<v|X>Y)+P(Y>X).P(X<u,Y<v|Y>X)

and not

P(U<u,V<v)=P(X>Y).P(Y<u,X<v)+P(Y>X).P(X<u,Y<v)

[ritu]

hello sir....can u pls suggest some good source for studying transformations?????????

[Amit Goyal]

Probability and Statistics by DeGroot
Or Mathematical Statistics by Freund
Or Statistical Inference by Casella and Berger

[SHIKHA]

yes sir answer matching bt wid a negative sign...what dis shows????

[SHIKHA]

SIR DEFINITELY DR IS A MISTAKE...EK TOH I DIDNT CONSISER V>U WHILE FINDING DISTRIBUTION..EST I DONT KNOW