# Questions tagged [complex-random-variable]

The tag has no usage guidance.

9 questions
Filter by
Sorted by
Tagged with
213 views

### Distribution of $e^{j\theta}$

Is there a canonical or analytic expression for the probability distribution for the circularly-symmetric complex random variable $Z$: $$Z = e^{j\theta},$$ where $\theta \sim \mathcal U(0, 2\pi)$? ...
305 views

### PSD of complex white gaussian noise

It may be a really simple question, but I'm not sure about this one: Given a complex white Gaussian noise process with iid real and imaginary parts and a double sided power spectral density of $N_0/2$...
31 views

### Variance of function of random variable

Is their an easier way to find variance of function of random variable? Till now what I am doing is first find probability density function of (function of random variable) then integrate over range.
29 views

### (For c-FastICA) On covariance and pseudocovariance matrix of a complex random vector

I am currently studying complex FastICA and the paper says that Suppose $\mathbf{s}$ is a $n\times1$ complex random vector. If $\mathbf{s}$ has zero mean, unit variance, and uncorrelated real and ...
72 views

### What is definition of independent random variable

I wan't to ask that if E{X}=0 E{Y}=0 and E{XY}=0 then how can I verify if the two random variables are independent or not. X , Y are both continuous random variables {I am not able to recall ...
39 views

### Clarifying matrix notation from an ICA-CMN paper

In the paper I am referring (and here from citeseer), complex vectors $\mathbf{z}$ and matrix $\mathbf{M}$ were defined as follows \begin{align} {{\bf z}} &= \left[z_{1},z_{2},\ldots,z_{N}\...
37 views

### Why is there only one integration in the solution if there is two integral in the formula?

In this problem the random variable is theta and according to the formula there should be two integrations but in the solution there is only one . Nor am i able to understand the meaning of x1 and x2 ...
Consider a complex random variable $Z=X+\jmath Y$, where the probability density function of $X$ and $Y$ are given by p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} {\rm e}^{-\frac{x^2}{2\sigma^2}}\quad\mbox{...