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

Correct Answer: 8

The correct answer is: 8