# Questions tagged [integral]

For on-topic question related to uses of the mathematical concept of an integral, i.e. $\int_a^b f(x)\; dx$. Purely mathematical questions about integrals are better asked at math SE: https://math.stackexchange.com/

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### Bounds of integration for the Wishart density

I once took a course that included zillions of exercises concerning the Wishart distribution, but as far as I recall, never mentioned the Wishart density. I asked something about that in this question,...
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### Understanding how to evaluate the integral causal-effect expression

I have this expression $$p( Y \mid \text{do}(Z=z)) = \int_{B, S, W, X} dBdSdWdX \ \ P(B | S) P(W | B, S) P(X | B, S, Z=z) \left[ \int_{Z'} dZ' P(Z'| B,S,W) P(Y | B, S, W, X, Z') P(S) \right]$$ ...
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### Does the negative multinomial distribution have a defined CDF?

I have a process that receives categorically distributed random inputs of 5 different types. The 5th type is considered "bad". If the process receives 4 bad inputs before receiving at least ...
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### Computing an integral that reduces to $\mathbb{P}[X>Y]$

Problem Evaluate $$I=\int_{-\infty}^\infty \frac{e^{-\frac{1}{2}\left(\frac{x-\mu)}{\sigma} \right)^2}}{\sigma \sqrt{2 \pi}}\frac{1}{1+e^{-x}}\, \mathrm{d}x$$ My attempt Now the first part of the ...
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### Probability that a random variable has a greater absolute value than the sample mean of iid random variable

I have encountered a problem which involves finding the probability that an observation of a random variable has a greater absolute value than the sample mean of an independent set of observations of ...
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### Best way or rules of thumbs for evaluating 1d integrals from randomly sampled grid points

I have a 1D domain (let's say the interval $(0,1)$) on which I randomly sample $N$ points from the uniform distribution. I have a function $f\colon (0,1) \to \mathbb{R}$ which is integrable. What is ...
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