Let X, X2, X, be a random sample from a discrete uniform population with probability mass...

 

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Let X₁, X2, X, be a random sample from a discrete uniform population with probability mass function 9-1 x=1,2,...,0, where 8 is an unknown parameter which is a positive integer. (a) Find an approximate two-sided 100(1-a)% confidence interval for 0. (b) Calculate an approximate two-sided 95% confidence interval for the small data set of n=4 observations: 155, 803, 243, 606. (c) Perform a Monte Carlo simulation to estimate the actual coverage for the arbitrary parameter settings 8=1000, 4 and 0.05. Use enough replications to achieve three digits of accuracy. FL Let X₁, X2, X, be a random sample from a discrete uniform population with probability mass function 9-1 x=1,2,...,0, where 8 is an unknown parameter which is a positive integer. (a) Find an approximate two-sided 100(1-a)% confidence interval for 0. (b) Calculate an approximate two-sided 95% confidence interval for the small data set of n=4 observations: 155, 803, 243, 606. (c) Perform a Monte Carlo simulation to estimate the actual coverage for the arbitrary parameter settings 8=1000, 4 and 0.05. Use enough replications to achieve three digits of accuracy. FL

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