Validating a Probability Mass Function
Given a discrete random variable X with possible values 1, 2, 3 and a probability mass function defined by \( P(X=x) = \begin{cases} a, & x=1 \\ 2a, & x=2 \\ 1-3a, & x=3 \end{cases} \) Determine the value of parameter a that makes this a valid pmf.