let f xy xy be a joint probability density function then 0

let f x,y (x,y) be a joint probability density function. then 0<= fx,y(x,y) <= 1 for all - infinite < x < infinite

a) true

b)false

Solution

Altjough f_X,Y(x,y) is a joint probability density function it has to follow the fundamental principle of probability.

We know that the value of any probability density function lies between 0 and 1.

So, f_X,Y(x,y) is nothing different from the normal probability density functions.

So its value will also lie between 0 and 1 for any value of X and Y.

If the value of f_X,Y(x,y) is less than 0 or greater than 1, then it is no more a joint PDF.

So, its a TRUE statement.

So, option (a) is correct.