Consider the likelihood of an i.i.d. sample from a Bernoulli population with parameter 𝑝 𝐿 ( 𝑥 1 , . . . , 𝑥 𝑇 ) = ∏ 𝑡 = 1 𝑇 𝑝 𝑥 𝑡 ( 1 − 𝑝 ) 1 − 𝑥 𝑡 . If you estimate the parameter 𝑝 using a Maximum Likelihood estimator, you obtain the point estimate 𝑝 ̂ = 1 𝑇 ∑ 𝑡 = 1 𝑇 𝑥 𝑡 , which corresponds to the sample mean. We know that for a Bernoulli random variable the expected value and the variance are 𝔼 ( 𝑥 𝑡 ) = 𝑝 , 𝕍 ( 𝑥 𝑡 ) = 𝑝 ( 1 − 𝑝 ) . Using this information, what is the variance of the estimator 𝕍 ( 𝑝 ̂ ) ?