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 k.(b) Find P `( X lt 2)` , P `( X le 2)` , P` (X ge 2 )`

Explanation

(i)As, we know,

Sum of all probablities in a probablity distribution is 1.
So, in this question,

`k+2k+3k+0 = 1=> 6k = 1`

`=> k = 1/6` which is the required value.



(ii)`(a)P(X<2) = P(X=0)+P(X=1)`

` = k+2k = 3k = 3(1/6) = 1/2`

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