CUET · MATHS · PYQ PAPER 2023
The random variable X has a probability distribution \(P(X)\) of the following form where \(k\) is a scalar:
\(P(X=x)=\left\{\begin{array}{ll}k, & x=0 \\ 2 k, & x=1 \\ 3 k, & x=2 \\ 0, & \text { otherwise }\end{array}\right.\)
Find \(P(X<2)\).
- A \(\frac{5}{6}\)
- B \(\frac{3}{4}\)
- C 1
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\sum P(X=x) = 1\) \(k + 2k + 3k = 1 \implies 6k = 1 \implies k = \frac{1}{6}\) \(P(X\(P(X\(P(X<2) = 3 \left(\frac{1}{6}\right) = \frac{3}{6} = \frac{1}{2}\)
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