As we know, for any probablity distribution,
`sumP(X) = 1`
So, for given distribution,
`0+k+2k+2k+3k+k^2+2k^2+7k^2+k=1`
`10k^2+9k-1=0`
`10k^2+10k-k-1=0`
`10k(k+1)-1(k+1)=0`
`(10k-1)(k+1) = 0`
As, k can not be negative, `k = 1/10`
(ii) `P(X<3) = P(X=0)+P(X=1)+P(X=2)`<br> ` = 3k = 3/10`
(iii) `P(X>6) = P(X=7)`
`=7k^2+k = 7/100+1/10 = 17/100`
(iv)` P(0ltXlt3)= P(X=1)+P(X=2)`
`=3k = 3/10`