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. $(3, \frac{3}{4})$ is a maximum likelihood estimator of $(m, p)$
• B. $(5, \frac{1}{4})$ is a maximum likelihood estimator of $(m, p)$
• C. $(5, \frac{3}{4})$ is a maximum likelihood estimator of $(m, p)$
• D. Maximum likelihood estimator of $(m, p)$ is NOT unique

Answer 1

Answer: (A)

$(3, \frac{3}{4})$ is a maximum likelihood estimator of $(m, p)$

Answer 2

The correct option is (A): $(3, \frac{3}{4})$ is a maximum likelihood estimator of $(m, p)$