Question:
If \(x\) follows a binomial distribution with parameters \(n = 100\) and \(p = \frac{1}{3}\), then \(P(X = r)\) is maximum when \(r\) equals
If \(x\) follows a binomial distribution with parameters \(n = 100\) and \(p = \frac{1}{3}\), then \(P(X = r)\) is maximum when \(r\) equals
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Mode of binomial: \(\lfloor (n+1)p \rfloor\) if \((n+1)p\) not integer.
Updated On: Apr 7, 2026
- 16
- 32
- 33
- None of these
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
For binomial, mode = \(\lfloor (n+1)p \rfloor\) or \(\lceil (n+1)p \rceil - 1\).
Step 2: Detailed Explanation:
\((n+1)p = 101 \times \frac{1}{3} = 33.67\)
Since \((n+1)p\) is not an integer, mode = \(\lfloor 33.67 \rfloor = 33\)
Step 3: Final Answer:
\(r = 33\).
For binomial, mode = \(\lfloor (n+1)p \rfloor\) or \(\lceil (n+1)p \rceil - 1\).
Step 2: Detailed Explanation:
\((n+1)p = 101 \times \frac{1}{3} = 33.67\)
Since \((n+1)p\) is not an integer, mode = \(\lfloor 33.67 \rfloor = 33\)
Step 3: Final Answer:
\(r = 33\).
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