Here is an estimator for the population average that might be applied when you know the data generating process produces only nonnegative numbers. Take each number in the sample, square it, find the average of the squared values, and take its square root. In equation form, the formula for this Weird estimator is
√(∑i=1nYi2/n)
Is this Weird estimator linear? Why or why not? Is it unbiased? A simple example that supposes there are only two possible, equally likely values for Yi will suffice to answer the question about bias.