Let X and Y be continuous random variables with joint density function
f(x,y)=(x)/(5)+cy, 0<x<1,1<y<50 - otherwiseend
where c is a constant. What is the value of c?

1 Answers

Best Answer

Since it has to be int int_(mathbb(R^(2))) f=1, we have that

1=int_(0)^(1)int_(1)^(5)((x)/(5)+cydy)dx=int_(0)^(1)((4x)/(5)+12c)dx=(2)/(5)+12c

which yield that c=(1)/(20).

Result:

c=(1)/(20)

1=int_(0)^(1)int_(1)^(5)((x)/(5)+cydy)dx=int_(0)^(1)((4x)/(5)+12c)dx=(2)/(5)+12c

which yield that c=(1)/(20).

Result:

c=(1)/(20)