The probability distribution of a random variable X is given below

(i) Determine the value of K .
(ii) Determine `P(Xle2)andP(Xgt2)`.
(iii) Find P`(Xle2)+P(Xgt2)`.

Explanation

We have,

(i) Since, `sum_(i=1)^(n)P_(i)=1,i=1,2,…..,nand P_(i)ge0`
`thereforek+k/2+k/4+k/8=1`
`rArr8k+4k+2k+k=8`
`therefore k=8/15`
(ii) `P(Xle2)=P(0)+P(1)+P(2)=k+k/2+k/4`
`=((4k+2k+k))/4=(7k)/4=7/4cdot8/15=14/15`
and `P(Xgt2)=P(3)=k/8=1/8cdot8/15=1/15`
(iii) `P(Xle2)+P(Xge2)=14/15+1/15=1`