Question 1178058
Must have {{{int( int(kxy, dx,1,2), dy,1,2) = k*int( int(xy, dx,1,2), dy,1,2) = k*(9/4) = 1}}}  ==> {{{k = 4/9}}}.

(i)  {{{P(X <= 3/2 , Y <= 3/2 ) = (4/9)*int( int(xy, dx,1,3/2), dy,1,3/2) = 25/144}}}


(ii) Quickly sketching the region defined by {{{ x+y <= 3/2}}} as well as the square region [1,2]x[1,2], you will see that these two regions do not intersect at all. Hence {{{P(X+Y <= 3/2) = 0}}}.

***In general, for this problem, {{{p(x,y) = (1/4)*(x^2 - 1)(y^2-1)}}}, 
where {{{1 <= x <= 2}}} and {{{1 <= y <= 2}}}.