# Tagged Questions

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### CDF of smallest eigenvalue of non-central Wishart matrix - how to evaluate the integral.

Expression 1 is needed to compute the cumulative distribution function of the smallest eigenvalue. What I am currently doing is integrating the non-central Wishart density function over the support ...
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### Integral of a bivariate normal cdf

Let $$\Phi_2(x,y;\rho):=\int_{-\infty}^y\int_{-\infty}^x \frac{1}{2\pi\sqrt{1-\rho^2}}e^{-\frac{1}{2(1-\rho^2)}(s^2+t^2-2st\rho)} \, ds \, dt$$ be the joint cdf of bi-variate normal random ...
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### Laplace transform of noncentral chi-square distribution

I'm interested in non central chi-square distribution. More specifically, i want to derive the laplace transform of noncentral chi-sqruae disribution or density function. Let me know whether it ...
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### The distribution of the inner product of a random complex normal vector.

Good day! I would like to find the distribution of the inner product of a random complex normal vector with: some constant vector; random gaussian vector. Let's assume a vector $\vec{z}$ which has ...
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### Difficult multivarate random variable - how to calculate it?

I have a random variable defined by $Y=\frac{\sum_{j=1}^{N}l_j \cos\theta_j}{\sum_{j=1}^{N}l_j\sin\theta_j}$ where $l_j \sim \text{log-normal-distribution} (\left \langle l \right \rangle, \sigma _l)$ ...
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### How to obtain a pdf of a random variable defined as a function of many variables?

Given $N$ independent random variables ($X_1$,$X_2$,...,$X_N$) with individual pdfs $f_1$,...,$f_N$: How to determine the pdf of a random variable $Y=G(X_1,...,X_N)$?
Given a plane with three points, $(0, -1)$, $(2,0)$, and $(0, 1)$ with $x$-axis and $y$-axis connecting three points to make a triangle. Suppose this triangle represents the support for a joint ...