If a random variable W only takes on the values 0,1,2,......,n-1 and its Probability Generating Function is p(t) = (t^n - 1)/{n(t - 1)}.
Determine P(W=2).
If a random variable W only takes on the values 0,1,2,......,n-1 and its Probability Generating Function is p(t) = (t^n - 1)/{n(t - 1)}.
Determine P(W=2).
You should know that $\displaystyle \Pr(W = w) = \left. \frac{1}{w!} \, \frac{d^w p}{dt^w} \right|_{t = 0}$.
In your question w = 2. The differentiation etc. is left for you to do.