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Using Properties of PMF to Find Unknown Parameters

STATS-GXGKDA

Determine the value of constant $k$ such that the following function $p(x)$ is a valid probability mass function:

$$ p(x)=\begin{cases} \dfrac{x+k}{20} &\mbox{if } x=.4,1, \mbox{ or } 1.6\\\ \\\ \dfrac{x}{2} &\mbox{if } x=.2 \mbox{ or } .6 \end{cases} $$

A

$k=1$

B

$k=2$

C

$k=3$

D

$k=4$

E

None of the above.