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## Homework Statement

Find λ given that the joint PDF of random variables X, Y, is given by:

[itex]f(x,y)=\lambda x y^{2}[/itex] where [itex]0\leq x\leq y\leq 1[/itex] and 0 otherwise

I have two questions:

1) How do I graph this? I'm not sure how to approach the inequality and graphing. What does this inequality actually? If you could provide a link to a site that might explain this graphing (specifically where there's multiple inequalities. I understand how to graph things with a single inequality, but I don't understand what the the multiple inequalities mean. I think it shows that both x and y are between 0 and 1 inclusive, but y is bigger than x. But how this translates graphically I'm not sure.

2) How can I integrate this? This is above question is an example, and it says that I can integrate it as follows:

[itex]\int_0^1 (\int_x^1 \lambda x y^{2} dy) dx = 1[/itex]

where it equals 1 by definition of a pdf. But I'm not sure about why they're the integral with respect to x starts from x.

Thanks!