Question

1. Let $X_1, X_2, \dots, X_n$ be an i.i.d sample from a distribution with the density function. $f(x) = \begin{cases} \frac{\theta}{(1+x)^{\theta+1}} & 0 \le x \le \infty, \theta > 0 \\ 0 & \text{Otherwise} \end{cases}$ Find the MLE estimate for $\theta$.

          1. Let $X_1, X_2, \dots, X_n$ be an i.i.d sample from a distribution with the density function.
$f(x) = \begin{cases} \frac{\theta}{(1+x)^{\theta+1}} & 0 \le x \le \infty, \theta > 0 \\ 0 & \text{Otherwise} \end{cases}$
Find the MLE estimate for $\theta$.

1. Let X1, X2, …, Xn be an i.i.d sample from a distribution with the density function.
f(x) = (θ)/((1+x)^θ+1) 0 ≤ x ≤∞, θ > 0
0 Otherwise
Find the MLE estimate for θ.

Added by Eduardo G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Dominador Tan

08/03/2023

Step 1

The likelihood function L(θ) for the given density function is the product of the density function evaluated at each observation, since the observations are independent and identically distributed (i.i.d). So, the likelihood function is: L(θ) = ∏(θ/(1+xi)^(θ+1)), Show more…

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Let x_(1),x_(2),dots,x_(n) be an i.i.d sample from a distribution with the density function. f(x)={(( heta )/((1+x)^( heta +1)),0<=x<=infty , heta >0),(0 Otherwise ):} Find the MLE estimate for heta . 1. Let X, X2,.... X, be an i.i.d sample from a distribution with the density function. A 0 xo,0>0 Otherwise 1+(x+1) Find the MLE estimate for 0.