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1 a markov chain is a special markov process explain2 explain the notion of a poisson process3 explain the
1 explain the relationship between the bernoulli and binomial distributions2 linear functions of normally distributed
1 explain the concept of the distribution of the sample2 explain why estimation testing and prediction amounts to
1 explain briefly the difference between descriptive statistics and statistical inference when faced with the problem
1 robustness is part of parametric statistical inference and is often believed part of non-parametric inference
1 compare and contrast parametric and non-parametric statistical inference2 non-parametric statistical models give rise
1 how does de finettis representation theorem provides a bridge between chance regularity and the notion of a simple
1 discuss von mises attempt to build a bridge between chance regularity and the notion of probability2 discuss de
1 explain briefly what a consistent estimator is what is the easiest way to prove consistency for estimators with
1 asymptotic normality of an estimator is an extension of the central limit theorem for functions of the sample beyond
1 explain the notion of the ideal estimator and explain intuitively how its definition relates to the properties of
1 comparing maximum likelihood and parametric method of moments estimators on efficiency grounds is not a very
consider the simple normal statistical modela derive the mles of microsigma2 and their sampling distributionsb derive
consider the simple laplace statistical model based on the probability modelderive the mle of u and compare it with the
consider the simple pareto statistical model based on the probability modelderive the mle of u and compare it with the
1 state the optimal properties of maximum likelihood estimators finite sample and asymptotic2 explain the difference
1 derive the iterative scheme for the score method in evaluating the mle first-order conditions in the case of the
1 discuss the notion of statistical adequacy and explain the role of misspecification testing in establishing it2
1 what do we mean by a uniformly most powerful test ump tests are scarceexplain2 explain the notions ofa unbiased test
1 how do we define an optimal test how is that related to the notion of an optimal estimator hint think of the ideal in
1 how does the neyman-pearson procedure solve the problem of a trade-off between the type i and type ii errors2 explain
1 explain the concept of a p-value as used by fisher2 a hypothesis of interest in a neyman-pearson test specified byis
1 compare a test as viewed by edgeworth and pearson what has pearson added to testing a hypothesis of interest2
two forces of magnitude 3p and 2p respectively acting at point have a resultant of rif the first force is doubled the
a cylinder with rigid well-insulated walls is divided into two parts by a rigid insulating wall with a small hole in it