CUET · MATHS · PYQ PAPER 2023
If a discrete random variable \(X\) has the following probability distribution: \(\begin{array}{lll}X & \frac{2}{3}^1 & \frac{4}{3} \\& & \\P(X) & & c \\& & c^2 \\& c^2\end{array}\) then \(c\) is:
- A \(\frac{1}{2}\)
- B \(\frac{1}{3}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\( c + c^2 + c^2 = 1 \) \( 2c^2 + c - 1 = 0 \) \( c = \frac{-1 \pm \sqrt{1^2 - 4(2)(-1)}}{2(2)} \) \( c = \frac{-1 \pm 3}{4} \) \( c = \frac{1}{2} \)
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