एक यादृच्छिक चर X का प्रायिकता बंटन निम्न्वत है-

ज्ञात कीजिए-
(i) k (ii) `P(Xgt3)`
(iii) `P(Xgt6)` (iv) `P(0ltXlt3)`

Answer

`(i) (1)/(10), (ii) (1)/(2), (iii) (17)/(100), (iv) (13)/(10)`

Explanation

(i) `overset(7)underset(x=0)Sigmap(k)=1`
`rArr" "k+2k+2k+3k+2k^(2)+k^(2)+7k^(2)+k=1`
`rArr" "10k^(2)+9k-1=0`
`rArr" "(10k-1)(k+1)=0`
`rArr" "k=(1)/(10)" या "k=-1`
`because k` ऋणात्मक नहीं हो सकता इसलिए `k=(1)/(10)`
(ii) `P(Xgt3)=P(X=4)+P(X=5)+(X=6)+P(X=7)`
`=3k+k^(2)+2k^(2)+7k^(2)+k`
`=(3)/(10)+(1)/(100)+(7)/(100)+(1)/(10)`
`=(4)/(10)+(1)/(10)=(5)/(10)=(1)/(2)`