i dont understand the reasoning behind the inequalities... The random variables

Question

i dont understand the reasoning behind the inequalities...

The random variables Y_1 and Y_2 have the joint probability density function f(y_1, y_2) = {6y^2_1y_2, 0 lessthanorequalto y_1 lessthanorequalto y_2, y_1 + y_2 lessthanorequalto 2 0, otherwise Use the given joint probability density function of Y_1 and Y_2 and show that the variables Y_1 and Y_2 are dependent. From the given inequalities 0 lessthanorequalto y_1 lessthanorequalto y_2, y_1 + y_2 lessthanorequalto 2 we have, If 0 lessthanorequalto y_1 1 then y_1 lessthanorequalto y_2 lessthanorequalto 2 - y_1 If 0 lessthanorequalto y_1 lessthanorequalto 1 then 0 lessthanorequalto y_1 lessthanorequalto y_2 If 0 lessthanorequalto y'_2 lessthanorequalto 2 then 0 lessthanorequalto y_1 lessthanorequalto 2 - y_2.

Explanation / Answer

For  inequalities we can understand as

we have 2  inequalities with function

0<=y1<=y2 and y1+y2<= 2

with that we can say 0<=y1,y2<=1

now

1)

if y1 is 0<= y1 <=1

we have condition that y1+ y2 <=2 or y2<=2 - y1

and y1<= y2 always hence

y1<=y2<=2-y1

by same logic we can explane ii and iii also

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