The random variable $X$ has a probability distribution $P(X)$ of the following form,where $k$ is some number:
$P(X) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$
Determine the value of $k$.

  • A
    $1/6$
  • B
    $1/3$
  • C
    $1/2$
  • D
    $1$

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