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

Explanation

AS Sum of all probabilities should be 1

`= k +2k+3k=1 rightarrow k =1/6`

(ii) `P(X<2)=P(X=0)+P(X=1)`
`
=k+2 k`
`
=3 {k}`
`
=frac{3}{6}`
`
=frac{1}{2}`
`
P(X le 2)=P(X=0)+P(X=1)+P(X=2) `
`
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