Question

For the distribution in HW 3, question 2, find (1 – a)100% asymptotic Cls based on the following distributions: i. The asymptotic distribution of the MLE using the asymptotic variance 020). ii. The asymptotic distribution of the MLE using the plug-in estimator for the asymptotic variance oz (Ô. (b) Consider X1, ..., Xn Poi(2). (i) Obtain a (1 – a)100% asymptotic confidence interval for .. (ii) Use the data from HW3, question 3(c), to report a 95% asymptotic confidence interval for 1 (your answer should be numeric values). i.i.d.

Answer 1

To find the (1-a)100% asymptotic Cls based on the given distributions, define the random variables X and X, and use the normal distribution to construct the confidence interval.

Step-by-step explanation:

To find the (1 – a)100% asymptotic Cls based on the given distributions, the first step is to define the random variables X and X in words. The random variable X represents the sample mean, and the random variable X represents the true population mean.

For this problem, the distribution to use is the normal distribution. The choice is based on the Central Limit Theorem, which states that the sample mean of a large enough sample will be approximately normally distributed regardless of the distribution of the original population.

To construct a (1 – a)100% asymptotic confidence interval, calculate the mean and standard deviation of the sample and then use the formula:

Confidence interval = sample mean ± (z-value * standard deviation) where the z-value is based on the desired confidence level and can be found using a standard normal distribution table or calculator.