Question

Let $f(x) = \frac{\theta}{x^2}$ on $[\theta, \infty)$. (a) Show that $f(x)$ defines a pdf for any $\theta > 0$. (b) Find the maximum likelihood estimator for the parameter $\theta$. (Hint: A differentiable function whose derivative is never zero is either always increasing, or always decreasing)

          Let $f(x) = \frac{\theta}{x^2}$ on $[\theta, \infty)$. 
(a) Show that $f(x)$ defines a pdf for any $\theta > 0$.
(b) Find the maximum likelihood estimator for the parameter $\theta$. (Hint: A differentiable function whose derivative is never zero is either always increasing, or always decreasing)

Let f(x) = (θ)/(x^2) on [θ, ∞).
(a) Show that f(x) defines a pdf for any θ > 0.
(b) Find the maximum likelihood estimator for the parameter θ. (Hint: A differentiable function whose derivative is never zero is either always increasing, or always decreasing)

Added by Ramon A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

12/05/2022

Step 1

$f(x) \ge 0$ for all $x \in [\theta, \infty)$. 2. $\int_{\theta}^{\infty} f(x) dx = 1$. Show more…

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Let $f(x) = \frac{\theta}{x^2}$ on $[\theta, \infty)$. (a) Show that $f(x)$ defines a pdf for any $\theta > 0$. (b) Find the maximum likelihood estimator for the parameter $\theta$. (Hint: A differentiable function whose derivative is never zero is either always increasing, or always decreasing)