Question

Let 𝑥1=2, 𝑥2=5 and 𝑥3=4 be the observed values of a random sample from a population having a probability mass function
$f(x;θ) =\begin{cases} θ(1-θ)^x, & \quad \text{if }x=0,1,2,...,,\\\ 0, & \quad Otherwise \end{cases}$
where 𝜃∈(0, 1) is an unknown parameter. If 𝜏̂ is the uniformly minimum variance unbiased estimate of 𝜃 2 , then 156 𝜏̂ equals ________

Answer 1

The correct answer is: 2