Question

Let 𝑥1=2.1, 𝑥2=4.2, 𝑥3=5.8 and 𝑥4=3.9 be the observed values of a random sample 𝑋1, 𝑋2, 𝑋3 and 𝑋4 from a population having a probability density function
$f(x) =\begin{cases} \frac{x}{θ^2}e^-\frac{x}{θ} & \quad \text{if }x >0,\\\ 0, & \quad Otherwise \end{cases}$
where 𝜃 ∈ (0, ∞) is an unknown parameter. Then, the maximum likelihood estimate of 𝑉𝑎𝑟(𝑋1) equals ________

Answer 1

The correct answer is: 8