Question

Let X and Y be two continuous random variables with joint pdf
f(x; y) =

cx2y(1 + y) for 0 6 x 6 3 and 0 6 y 6 3
0; otherwise:
(a) Find the value of c:

(b) Find the probability P(1 6 X 6 2; 0 6 Y 6 1):

Answer 1

Answer:

c = 3

Step-by-step explanation:

To find the constant cc, we write

1=∫∞−∞∫∞−∞fXY(x,y)dxdy=∫10∫1−x0cx+1dydx=∫10(cx+1)(1−x)dx=12+16c.1=∫−∞∞∫−∞∞fXY(x,y)dxdy=∫01∫01−xcx+1dydx=∫01(cx+1)(1−x)dx=12+16c.

Thus, we conclude c=3