题目
题目

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 8. Quiz for Class 8

单项选择题

What's the variance of the average of n points of  random variables X. All X's are independent and identically distributed. That is, what's V(), for i = 1 to n? ____________________________________________________ (reminder: )

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Question restatement: What's the variance of the average of n points of random variables X, where all X's are independent and identically distributed? That is, what's V(X̄) for i = 1 to n, with X̄ = (X1 + X2 + ... + Xn)/n. Step 1: Consid......Login to view full explanation

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What's the variance of the average of n points of X. All X's are independent and identically distributed. That is, what's V(xbar)?

What's the variance of the average of n points of  random variables X. All X's are independent and identically distributed. That is, what's V( ¯ X ), for i = 1 to n? ____________________________________________________ (reminder: )

Consider the likelihood of an i.i.d. sample from a Bernoulli population with parameter p L(x1,...,xT)= T ∏ t=1pxt(1−p)1−xt. If you estimate the parameter p using a Maximum Likelihood estimator, you obtain the point estimate ˆ p = 1 T ∑ T t=1 xt, which corresponds to the sample mean. We know that for a Bernoulli random variable the expected value and the variance are 𝔼(xt)=p, 𝕍(xt)=p(1−p). Using this information, what is the variance of the estimator 𝕍( ˆ p )?

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