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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

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Best estimator for a 3 coin problem

Let $X,Y,Z$ be three unfair coins. We consider the coin $\Gamma=XI(Z=1)+YI(Z=0).$ We are given the sample $S=\{(\Gamma_i,Z_i)| i \leq n \}$ Let $k=\sum_{i \leq n}I(Z_i=1)$. For every pair of $(\Gamma_ …
Thomas Eberhard's user avatar