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15
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Show that $d_2$ is the Bayes rule if the posterior mean of $\theta$ is greater than $1/2$.

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#probability #probability-theory #statistics #probability-distributions #statistical-inference
130
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Understanding the density function and expected value of an estimator.

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#probability #probability-theory #statistics #probability-distributions #statistical-inference
221
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About L2 error distribution and its STRANGE oscillatory behaviour

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#statistical-inference #error-function #chi-squared
617
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Derive a sufficient statistic for $\theta$.

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#statistics #probability-distributions #statistical-inference
58
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Rejecting null based on the likelihood ratio test

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#statistics #statistical-inference #hypothesis-testing
484
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Uniformly minimum variance unbiased estimator of theta.

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#statistics #statistical-inference
93
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Show that the posterior probability of $H_0$ equals $\Phi\left(\sqrt{n}\frac{\theta_o -\bar{X}_n}{\sigma}\right)$

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#probability #probability-theory #statistics #probability-distributions #statistical-inference
218
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Derive an expression for the $p$-value using a test with test statistic $T =\sqrt{n}(\bar{X}_n - \theta_0)/\sigma$

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#probability #probability-theory #statistics #probability-distributions #statistical-inference
104
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Derive the posterior density of $\Theta$.

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#probability #probability-theory #statistics #probability-distributions #statistical-inference
155
Views

Transformation of MVN random variable

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#random-variables #statistical-inference
215
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Show that $\hat{\theta}$ is not minimax.

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#probability #probability-theory #statistics #probability-distributions #statistical-inference
58
Views

Order statistics, unclear derivation of the distribution function, uniform df

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#probability-theory #statistics #statistical-inference #order-statistics
260
Views

Show that $T(X) = \min(X_1,\ldots,X_n)$ is a sufficient statistic using the factorisation theorem.

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#probability #statistics #probability-distributions #statistical-inference
1.1k
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Expected Value for a combination of IID from $f(x,\theta) = \frac{ \theta }{x^{ \theta + 1}}$

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#probability #statistics #probability-distributions #statistical-inference
259
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Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$

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#probability #statistics #statistical-inference #uniform-distribution #variance

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