The probability distribution of X is:

We Know that

Therefore,

⇒ 2p+2p+3p+p² +2p² +7p² +2p=1

⇒ 10p² +9p-1=0

⇒ 10p² +10p-p-1=0

⇒ 10p(p+1)-1(p+1)=0

⇒ (10p-1)(p+1)

10p-1=0 or p+1=0

We considered because p is a probability and probability cannot be in negative

Option (B) is incorrect because p is a probability and probability cannot be in negative

Option (C) is incorrect because p is a probability and probability cannot be in negative

Option (D) is incorrect because by putting , the sum total of pxi is not equal to 1