Dragonite

### Questions (8)

 3 Upper bound on $P(n^{-1}\sum_{i=1}^n (X_i - \lambda_i)>t)$ for independent $X_i\sim\operatorname{Poisson}(\lambda_i)$ 3 Let $X_i$, $i=1,\dots,n$ be i.i.d. normal $N(\mu,\sigma^2)$ where $\sigma$ is known, use Gaussian prior on $\mu$ to find Bayes estimator 2 Let $X$ be $n \times p$ with rank$(X)=k$, $\epsilon \sim N(0,I_p)$ be a vector with i.i.d. Show $E\|\ X\epsilon \|_2^2 = \sum_{j=1}^k \sigma_j^2$ 1 Does Hoeffding or Bernstein inequality provide a more accurate bound for this problem? 1 Show that $X \sim \chi^2(1)$, the chi-squared random variable with one degree of freedom, is a sub-exponential $(4,4)$ random variable

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### Tags (8)

 0 mathematical-statistics × 6 0 probability × 2 0 bayesian × 2 0 mgf 0 poisson-distribution × 2 0 probability-inequalities 0 random-variable × 2 0 independence

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