Change of discrete random variables I just read this:
Let X be a discrete random variable whose probability function is $f(x)$. Suppose that a discrete random variable U is defined in terms of X by $U = \phi(X)$, where to each value of X there corresponds one and only one value of U and conversely, so that $X = \psi (U)$. Then the probability function for U is given by $g(u) = f [\psi(u)]$.
Is this correct? This is from Schaum's  Probability and Statistics 4th edition pg42.
Can any of you please help me understand this? I am sorry I am a bit weak in Probability. Thanks!

Yes, it is correct. There exists a one-to-one mapping between X and U which can be undone or inverted. So the probability functions for both X and U take the exact same shape.
For e.g U could be as simple as a scaled version of X , e.g U = 2X.
