題組內容

2. (5% each, 15% in total) Consider a random variable $X$ with the PMF $$P_X(x) = \begin{cases} c & \text{if } x = 1; \\ \binom{1}{2}^x & \text{if } x = 2, 3, 4 \cdots; \\ 0 & \text{else}, \end{cases}$$ for some constant $c$.

(b) What is the probability \( P[X \in \{0,1\}] \)?