Interval Estimation - Confidence interval for the mean of normal population

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Interval Estimation - Confidence interval for the mean of normal population
for large and small samples, when sigma the population standard deviation is known and unknown
  1. Easy Statistics
  2. confidence interval
  3. interval estimation
  4. estimation theory
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Show that by an example of each case where the estimate
a) NOT UNBIASED BUT NOT CONSISTENT
b) UNBIASED BUT NOT CONSISTENT
2)derive the confidence interval for the proportion of a Binomial population
3) How do you test the equality of variances of two normal populations?
4) Derive the maximum likelihood estimate of the parameter of Normal population
5)Examine whether f(x) = (1+theeta)x^theeta, 0<x<1 admits a maximum variance of any unbiased estimator of theeta from this population
6) obtain the maximum likelihood estimates & moment estimates of parameter of normal distribution

John_