The problem involves a rectangle in the x-y plane with dimensions H=1 and L=2, where the task is to find a line or diagonal such that for every point in the shaded area below that line, the condition x>y holds. There is some ambiguity regarding the placement of the rectangle and its implications for the solution.
The discussion is ongoing, with participants exploring the implications of the rectangle's position in the plane. Some guidance has been offered regarding the intersection point, but there is no consensus on the overall approach due to the lack of clarity about the rectangle's placement.
Participants note that the problem cannot be fully addressed without knowing the specific location of the rectangle in the x-y plane, as this affects the interpretation of the line and the shaded area.
Is there a pitcher associated with this problem that hasn't been attached?TheMathNoob said:Homework Statement
There is a rectangle in the x-y plane with dimensions H=1, L=2. Find a line or diagonal in the rectangle in which for every point in the shaded area below that line x>y.
Homework Equations
The Attempt at a Solution
The line has to intersect a point in y=1 in which x>y. This point would be (1,1). But I do not get why.
Suppose that the joint p.d.f. of a pair of random variables (X, Y) is constant on the rectangle where 0≤x ≤2 and 0≤y ≤1, and suppose that the p.d.f. is 0 off of this rectangle.SteamKing said:Is there a pitcher associated with this problem that hasn't been attached?
Not sure I understand your question. I wouldn't worry about the distinction between > and >= here.TheMathNoob said:The line has to intersect a point in y=1 in which x>y. This point would be (1,1). But I do not get why.
It is impossible to answer this without knowing where the rectangle is. The same size rectangle placed at different places in the plane will give different answers.TheMathNoob said:Homework Statement
There is a rectangle in the x-y plane with dimensions H=1, L=2. Find a line or diagonal in the rectangle in which for every point in the shaded area below that line x>y.
2. Homework Equations
The Attempt at a Solution
The line has to intersect a point in y=1 in which x>y. This point would be (1,1). But I do not get why.