We have a coin and a dice, both are fair, and we declare $X$ and $Y$ so they correspondingly describe the events $X=1$ and $X=0$ wheter we get Heads or Tails and $Y=\text {outecome from dice 1, 2, 3, 4, 5, 6}$. We also declare $Z=XY$
I need to find the range of $Z$ and compute its mass. Also, i need to find its average value and variance.
I think range of $Z$ is {${0, 1, 2, 3, 4, 5, 6}$.}
I haven't really understood this chapter in probability yet. A little help for the first part of my question would be very helpful to move on to the next questions.