Consider a random variable $X$ which can take only non zero integer values from -20 to +20, and whose probability distribution is symmetric around 0. Suppose the function $f(x)$ is the probability mass function of X. Now consider the random variable $Y= X^2$. Derive the relationship between g(y) and f(y).
Since $Y= X^2$, do we have g(y) = f($\sqrt y$)? Can we derive probabilities like this?