Question

In addition can you please explain how you found the bounds?

density: Let X and Y be jointly continuous with the following joint - 420x²y3 ,X>0, y>o ,x+yal C o otherwise ① set up the double integral to find P(x2.5,4>,25). ③ Find E(xy)

Answer 1

f(xoy) - 420x²y x>0, y>o, x+yal 1 0 ; olourse Bounds xtyal axal-fie, o cxalty (since the lower bound of x is o) Since y is dependent on xe, the lower bound for y is 0 ( y>o) If the upper bound of x is l-y, the value of y cannot exceed 1 or less than o, hence the upper bound of y is . 1.e, ocycl 0.25 0.5 (a) P(x<0.5, 420.25)= [(420x²y3 dx dy. o o 0.25 0.25 = 0.0171 +420 727. "dy. 40 Jys costo") dy 140 fo.125y'dy: 17.5.73035 - 4.345 [0.25"} P(x<0.5, YC 0,25) = 0.0171 (6) E (xy) - ssxy, 420 x ²4² de dy +420 3 * * dx dy - 420 421 dy = 105 Jy" (1-4) "dy. = 105 fy" (1-4y + by - wy?t yu) dy 11-4

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