Question:
A biased coin, with probability of head as \( p \), is tossed \( m \) times independently. It is known that \( p \in \left\{ \frac{1}{4}, \frac{3}{4} \right\} \) and \( m \in \{3, 5\}. \) If 3 heads are observed in these \( m \) tosses, then which of the following statements is correct?
A biased coin, with probability of head as \( p \), is tossed \( m \) times independently. It is known that \( p \in \left\{ \frac{1}{4}, \frac{3}{4} \right\} \) and \( m \in \{3, 5\}. \) If 3 heads are observed in these \( m \) tosses, then which of the following statements is correct?
Updated On: Oct 1, 2024
- \((3, \frac{3}{4})\) is a maximum likelihood estimator of \((m, p)\)
- \((5, \frac{1}{4})\) is a maximum likelihood estimator of \((m, p)\)
- \((5, \frac{3}{4})\) is a maximum likelihood estimator of \((m, p)\)
- Maximum likelihood estimator of \((m, p)\) is NOT unique
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The Correct Option is A
Solution and Explanation
The correct option is (A): \((3, \frac{3}{4})\) is a maximum likelihood estimator of \((m, p)\)
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