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The random variable X has a probability ...

The random variable X has a probability distribution P(X) of the following form, where k is some number :
`P(X)={{:(k, "if " x=0),(2k, "if " x=1),(3k, "if " x=2),(0, "otherwise"):}`
(a) Determine the value of k.
(b) Find `P (X lt 2), P (X le 2), P(X ge 2)`.

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The correct Answer is:
`(a) (1)/(6), (b) (1)/(2)`
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