Been going through a question I have the answer to but no working from an exercise book... can't see the logic. Wonder if anyone can lend an eye?
Q:Let be a random point chosen uniformly on the region
a) Sketch R
b) Find the marginal densities of X & Y
c) Find the conditional density of Y given X
a) simply a kite shape with vertices at (-1,-1),(-1,1),(1,1) & (1,-1)
b) Evaluate joint density function:
By observation, the area is a tilted square with sides 1 x1 => area = 1 =>
over , now this makes sense to me, as we integrate of the 0 and (1-mod(y)) as limits given by initial conditions. By symetary, marginal of Y is the same except Y instead of X in the expression.
surely this gives the reciprocol of the marginals already found ie:
The answer in the back of the book is:
Now I can understand the range of y, but cant seem to see where the conditional comes from..... would make my day if someone says its a typo lol
Thanks for reading.