Question

Let 0.2, 1.2, 1.4, 0.3, 0.9, 0.7 be the observed values of a random sample of size 6 from a continuous distribution with the probability density function
$f(x) = \begin{cases} 1, & 0< x \le \frac{1}{2} \\\ \frac{1}{2\theta-1}, & \frac{1}{2} \lt x \le \theta \\\ 0, & \text{otherwise,}\end{cases}$
where θ > $\frac{1}{2}$ is unknown. Then the maximum likelihood estimate and the method of moments estimate of θ, respectively, are

• A. $\frac{7}{5}$ and 2
• B. $\frac{47}{60}$ and $\frac{32}{15}$
• C. $\frac{7}{5}$ and $\frac{32}{15}$
• D. $\frac{7}{5}$ and $\frac{47}{60}$

Answer 1

Answer: (C)

$\frac{7}{5}$ and $\frac{32}{15}$

Answer 2

The correct option is (C) : $\frac{7}{5}$ and $\frac{32}{15}$.