List questions from probability-distributions

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Given is density - Create a random variable with it

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Transform Logistic/Sigmoid function

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Probability density function of any point inside a hypersphere.

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Listing all sets in sigma-algebra of a random variable when there are similar mappings?

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Determining the measurable space and density function for an event

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Proof of an identity in probability theory

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Show that $\hat{\theta}$ is not minimax.

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Bayesian updating - likelihood

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Upper bound for $\mathbb{E}[e^{-aX}]$, where X follows binomial distribution $B(n,p)$

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

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Marginals of the PDF $f(x,y) = \frac{3}{2}(x^2 y + y)$ for $x,y \in [0,1]$

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Probability density function of a triangle with unknown height

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Expected Value for a combination of IID from $f(x,\theta) = \frac{ \theta }{x^{ \theta + 1}}$

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Two random variables generated with common random varibales

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List Question

p-test and basic probability

Given is density - Create a random variable with it

Transform Logistic/Sigmoid function

Probability density function of any point inside a hypersphere.

Listing all sets in sigma-algebra of a random variable when there are similar mappings?

Determining the measurable space and density function for an event

Proof of an identity in probability theory

Show that $\hat{\theta}$ is not minimax.

Bayesian updating - likelihood

Upper bound for $\mathbb{E}[e^{-aX}]$, where X follows binomial distribution $B(n,p)$

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

Marginals of the PDF $f(x,y) = \frac{3}{2}(x^2 y + y)$ for $x,y \in [0,1]$

Probability density function of a triangle with unknown height

Expected Value for a combination of IID from $f(x,\theta) = \frac{ \theta }{x^{ \theta + 1}}$

Two random variables generated with common random varibales

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