Question

et X and Y be continuous random variables having joint density functio

Answer 1

To find the constant c, we write

$1=∫^∞_{−∞}∫^∞_{−∞}f_{XY}(x,y)dxdy\\ 1=∫^1_0∫^{1−x}_0cx+1dydx\\ 1=∫^1_0(cx+1)(1−x)dx\\ 1=\frac{1}{2}+\frac{1}{6}c.$

Thus, we conclude c=3