At first, we check that ∬R2f(x,y)dxdy=1. ∬R2f(x,y)dxdy=∫01∫0x8xydydx=∫014x3dx=x4∣01=1. The marginal probability density of Y is: fY(y)=∫Rf(x,y)dx=∫y18xydx=4yx2∣y1=4(y−y3).
Answer: the marginal probability density function of Y is: fY(y)=4(y−y3).
Comments
Leave a comment