Answer:
f(x,y) = 5x⁴(2y³ +y ) 0<x<1 , 0<y<1 , 0 otherwise
Step-by-step explanation:
Given
F(x) = 5x⁴ for 0<x<1 and 0 otherwise
f(y)= 2y³ +y for 0<y<1 and 0 otherwise
the joint p.d.f is given by
f(x,y) = f(x) * f(y)= 5x⁴(2y³ +y ) 0<x<1 , 0<y<1 , 0 otherwise
The joint pdf is found by multiplying the marginal pdfs.
The two random variables are said to be statistically independent if the joint probability function can be expressed as the product of two marginal functions.
