The random variable X has a probability distribution P(X) of the following form, where k is some number : \[ P(X) = \left\{ \begin{array}{l l} k & \quad \text{if $x$ = 0}\\ 2k & \quad \text{if $x$ = 1} \\ 3k & \quad \text{if $x$ = 2} \\ 0 & \quad \text{otherwise} \end{array} \right. \] (a) Determine the value of k. (b) Find $P (X \lt 2), P (X \leq 2), P(X \geq 2).$

Question

$\begin{array}{1 1} (a) \large \frac{1}{6} \quad \normalsize(b) \; \large\frac{1}{6}, 1, \large\frac{1}{6} \\(b) \large \frac{1}{6} \quad \normalsize(b) \; \large\frac{1}{2}, 1, \large\frac{1}{2} \\(c) \large \frac{1}{3} \quad \normalsize(b) \; \large\frac{1}{3}, 1, \large\frac{1}{6} \\ (d) \large \frac{1}{3} \quad \normalsize(b) \; \large\frac{1}{3}, 1, \large\frac{1}{3}\end{array} $