The probability distribution of random variable X with two missing probabilities p₁ and p₂ is given below: It is further given that P ( X 2)=0.25 and P ( X 4)=0.35 . Consider the following statements: array ll I. p₁=p₂ & II. p₁+p₂= P ( X =3) array Which of the statements given above is/are correct?

Step-by-step solution

Subtracting equation (ii) from equation (i) aligned k+ P ₁ & =0.25 ...(i) 2 k+ P ₂ & =0.35...(ii) - - & - -k+ P ₁- P ₂ & =-0.10 aligned k+ P ₂- P ₁=0.10 ...(iii) aligned & k+ P ₁+4 k+ P ₂+2 k=1 & 7 k+ P ₁+ P ₂=1...(iv) aligned Adding the equations (iii) and (iv) aligned 7 k+ P ₂+ P ₁ & =1 k+ P ₂- P ₁ & =0.10 8 k+2 P ₂ & =1.1 aligned aligned & 4 k+ P ₂=0.55 & P ₂=0.55-4 k aligned From (ii) gathered 2 k+0.55-4 k=0.35 k=0.10 gathered Now aligned & P ₂=0.55-4 .10 & P ₂=0.15 aligned From (i), P ₁=0.25-k P₁=0.15