Question

g Given the following joint density functions of X and Y, determine whether X and Y are independent:Independent, not independent, independent, independent Not independent, independent, independent, independent Independent, not independent, independent, not independent Not independent, independent, independent, not independent None of above g

Answer 1

The given joint density functions of X and Y are not independent.

The option "not independent not independent" is correct

Explanation:

Given that Joint density functions of X and Y.

To determine whether the given random variables X and Y are independent :

X and Y are not independent

For :

• Generally two random variables X and Y are jointly continuous if they have a joint probability density function as defined below.

• The function
  `f_(XY)(x,y)` is called the joint probability density function (PDF) of X and Y.

• X and Y are NOT independent in joint probability density function.

Therefore the given joint density functions of X and Y are not independent

Therefore option "not independent not independent "is correct