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,""""ot h e r w i s e` (a) Determine the value of k. (b) Find

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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