Basic stats question

[Homer Simpson]

Can an unbiased, inefficient estimator of population mean be a consistent estimator?

[Akshay Jain]

Consistent estimator means that the estimator converges to the population parameter in probability as sample size increases and unbiased means that the expectd value of estimator is equal to the population parameter.....
and efficiency of an estimator is ragarding the variance of distribution of estimator
even if the estimator is inefficient it is possible that it is unbiased and consistent
for example if u look at the maximum likelihood estimators of regression coefficients, they are unbiased and consistent but inefficient