Question

Let 2.5, -1.0, 0.5, 1.5 be the observed values of a random sample of size 4 from a continuous distribution with the probability density function
$f(x)=\frac{1}{8}e^{-|x-2|}+\frac{3}{4\sqrt{2\pi}}e^{-\frac{1}{2}(x-\theta)^2},\ \ x \in \R,$
where θ ∈ $\R$ is unknown. Then the method of moments estimate of θ equals __________ (round off to 2 decimal places)

Answer 1

The correct answer is 0.48 to 0.52.(approx)