"Suppose X be arandom variable and Y be adiscreterandom varaible. Let f_X,Y (x,y) denote the joint density function of X and Y..."continuous

I'm not sure if I understand the meaning of joint density here. In the case above, what does the joint density mean? What are the properties of it? Does it still double integrate to 1 (like for the jointly continuous case)?

From my probability class, I remember that a joint density function is only defined in the case when X and Y are BOTH continuous random variables. But when one random vaiable is continuous and the other discrete, how do we even define the joint density function?

Hopefully someone can explain this.

Thank you!