एक यादृच्छिक चर X का निम्नलिखित प्रायिकता बंटन है :
`{:(X,0,1,2,3,4,5,6,7),(P(X),0,k,2k,2k,3k,k^(2),2k^(2),7k^(2)+k):}`
ज्ञात करें (i) k (ii) `P(Xgt6)` (iii) `P(0ltXlt3)`

Explanation

(i) `underset(X=0)overset(7)SigmaP(X)=1`
`implies0+k+2k+2k+3k+k^(2)+2k^(2)+(7k^(2)+k)=1`
`implies 10k^(2)+9k-1=0implies(k+1)(10k-1)=0`
`implies k=(1)/(10)" "[because kgt0]`
(ii) `P(Xgt6)=P(X=7)=7k^(2)+k=(7)/(100)+(1)/(10)=(17)/(100)`
(iii) `P(0ltxlt3)=P(X=1)+P(X=2)`
`=k+2k=3k=(3)/(10)`