A random variable has the following probability distribution: `X=x_i :\ \ 0 \ \ 1 \ \ 2 \ \ 3 \ \ 4 \ \ 5 \ \ 6 \ \ 7` `P(X=x_i):0 \ \ 2p \ \ 2 p\ \ 3p\ \ p^2\ \ 2p^2 \ \ 7p^2 +p` The value of `p` is a. `1/10` b. `-1` c. `-1/10` d. `1/5`

Explanation

`Sigma_{x=0}^{7} P(x)=1`


`therefore P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)=1`


`therefore 0+p+2 p+2 p+3 p+p^{2}+2 p^{2}+7 p^{2}+p=1`


`therefore 10 p^{2}+9 p-1=0`


`therefore 10 p^{2}+10 p-p-1=0`


`therefore 10 p(p+1)-1(p+1)=0`


`therefore(p+1)(10 p-1)=0`


`therefore 10 p-1=0`


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