Probability mass function

Let values from 0 to 9 with equal probability of 0.1 make up the elements of a discrete random variable $Y$, and let discrete random variable $Z$ be a mod 3 of random $Y$ as $Z\equiv Y \pmod{3}$. Calculate $p_Z(z=1)$. Round your answer to 1 decimal figure.

Tip:

The modulus or "mod" operator gives the remainder after dividing one number by another.

Example: Dividing 7 by 3 gives remainder 1, and it is written as: 7 mod 3 = 1.

In the example you should apply a mod 3 for all values in the random variable $Y$in order to associate values for the random variable $Z$.