Question

A random variable is uniformly distributed over (-1,1) and Y = X2 . Determine whether X and Y are correlated

Answer 1

Step-by-step explanation:

Solution:From Equation (2.18), since

f(a)=g(a){ 1, 0<a<a 0, otherwise

we obtain

fX+Y(a)=∫

1

0

f(a−y) dy

For 0≤a≤1, this yields

fX+Y(a)=∫

1

0

dy=a

For 1<a<2, we get

fX+Y(a)=∫

1

a−1

dy=2−a

Hence,

fX+Y(a)={ a, 0≤a≤1 2−a, 1<a<2 0, otherwise

Rather than deriving a general expression for the distribution of X+Y in the discrete case, we shall consider an example.