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Order statistics of independent but non-identical uniform distribution
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Denote $X_{(1)}$ as any first observation from the original sample, $X_{(2)}$ as any second observation etc. We can calculate the probability as follows: \begin{align}P(X_j&=X_{n-i+1,n})\\ &=\...

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Conditional expectation given event and random variable
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I will post this as an answer to my own question, but I am not entirely sure if it is correct. $\mathbb{E}(Y|W=1, X)$ is the random variable defined by having the property: $$\int_B \mathbb{E}(Y|W=1,...

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