The probability mass function of a random variable X is given by P(X = x) = ⁵C_x 2^5 , for x = 0, 1, 2, 3, 4, 5 and = 0 , otherwise. Then which of the following is correct?

Step-by-step solution

The given probability mass function is P(X = x) = ⁵C_x 2^5 . We evaluate P(X 2) and P(X 3) . P(X 2) = P(X = 0) + P(X = 1) + P(X = 2) P(X 3) = P(X = 3) + P(X = 4) + P(X = 5) Using the property of combinations ^ n C_r = ^ n C_ n-r , we have: ⁵C₀ = ⁵C₅ P(X = 0) = P(X = 5) ⁵C₁ = ⁵C₄ P(X = 1) = P(X = 4) ⁵C₂ = ⁵C₃ P(X = 2) = P(X = 3) Adding the corresponding terms gives: P(X = 0) + P(X = 1) + P(X = 2) = P(X = 3) + P(X = 4) + P(X = 5) P(X 2) = P(X 3) Answer: p(x 2) = p(x 3)