# Tagged Questions

Questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution.

0answers
30 views

### How to fit a gaussian model on the overlapped area of two separate gaussians?

Suppose I have two 1D Gaussians distribution with N(U1,S1) and N(U2,S2) where U is the mean and S is the standard deviation. Suppose if we draw these two Gaussians, they overlap on a interval. Now ...
0answers
22 views

### How to estimate a normal distribution with mixture of gaussians?

I have a set of points which I can fit a Gaussian model on them using Maximum likelihood estimation. but this estimation is weak and I want to improve it. I want to fit a mixture of Gaussian on these ...
1answer
32 views

### Standard deviation misunderstanding

Here is a question that I stumbled upon (and the solution to it, my reasoning follows after the image): I answered "The two quantities are equal". My reasoning was as follows: the question mentions ...
1answer
157 views

### Bivariate normal distribution of points

I would like to generate points (x,y) in a 2-D plane that has a circular normal distribution similar to this: I found multiple terms for describing a "circular normal distribution" and yet, I'm not ...
0answers
84 views

### Normal and poissonian probability problems

I am working on a problem with a normal probability distribution but I am unsure of the results I calculated the probability asked for but still hesitate regarding the output and especially the first ...
0answers
11 views

### Finding Conditional Distribution of Multivariate distribution

Q: Supposing y ~ N4 (µ,∑) and µ = (1 2 3 -2)' ∑ =\begin{pmatrix} 4 & 2 & -1 & 2\\ 2&6&3&-2\\ -1&3&5&-4 \\ 2 &-2 &-...
2answers
402 views

### Normal Distribution: Probability of a Negative Value

The random variable $X$ can take negative and positive values. $X$ is distributed normally with mean $3$ and variance $4$. How can I find the probability that $X$ has a negative value?
0answers
31 views

### Proving that a subvector in a multivariate Normal distribution is also a Normal Distribution

Q: Assuming y = [y1 , y2, .. , yp]' is a p-dimensional random vector with mean vector µ and covariance matrix ∑. Given for any a = [a1, a2, .., ap]', we have a'y ~ N[a'µ, a'∑a]. Show ...
1answer
33 views

### Random variable with density function that is scaled geometric mean of density functions of two independent normally distributed random variables

Given two independent normally distributed random variables A and B: $$A \sim \mathcal{N(\mu_A, \Sigma_A)}$$$$B \sim \mathcal{N(\mu_B, \Sigma_B)}$$ is there a way to find normally distributed random ...
1answer
104 views

0answers
38 views

### normal distribution under special condition

Given independent Gaussian random variables $U\sim N(−1,1)$ and $V\sim N(1,1)$, are the 2-element vector $T=(U+V, U−2V)$ and the variable $$W= U\text{ with 50% chance}, V \text{ with 50% chance}$$ ...
2answers
52 views

### Normal distribution with standard deviation = I

Suppose a vector $\epsilon \in \mathbb R^d$ is a random vector drawn from the isotropic normal distribution: $\epsilon$ ~ $\mathcal N (0, I)$ [As in Eq. 1.34 here.] I suppose ...
2answers
61 views

### How does the formula for standard deviation result in the normal distribution

Trying to understand this is in a high school level. I understand that the how $\frac {\Sigma|x-\bar x|}{n}$ calculates the mean of the distances of each score to the mean. I use this idea to map ...
0answers
11 views

### How to calculate distribution of (X1, X2) conditional on (C1, C2)?

Say that $X_{1}$ = $a_{1}$$X_{2} + B_{1}$$C_{1}$ + $E_{1}$  , and         $X_{2}$ = $a_{2}$$X_{1} + B_{2}$$C_{2}$ + $E_{2}$  , ...
0answers
71 views

2answers
48 views

### Using Normal Distributions to find Proportion

The height of a randomly selected woman from a population is normal with $\mu=165cm$ and $\sigma=7cm$. The heights f the men in this population are normal with $\mu=178cm$ and $\sigma = 8cm$. I am ...
2answers
26 views

### Generating points from 2 Normal distributions and $0$-probability continuous r.v.s

Consider the following experiment: We generate "green" points and "blue" points in $\mathbf{R}$ using two different normal distributions as follows: 1000 green points are sampled from a $N(-1, 1)$ ...
1answer
443 views

### Understanding the matrix normal distribution

A random $n \times p$ matrix $X$ is distributed according to a matrix valued normal distribution iff $\mathrm{vec}(X) \sim \mathcal{N}_{np}(\mu, V \otimes U)$, where $\mu \in \mathbb{R}^{np}$ is a ...
1answer
61 views

### If $X$ and $Y$ are Normally distributed with correlation $\rho$, can we say anything about $E[Y \mid X]?$

Let $X \sim N(0, 1)$ and $Y \sim N(0, 1)$ and $\mathbb E[XY]=\rho$. Can one say anything about the conditional expectation $\mathbb E[X \mid Y]$? In general, this clearly does not seem to work, ...
0answers
132 views

1answer
60 views

### What is the correct equation for “Normal distribution function of continuous random variable”?

I was reading a book and came across with a equation which gives the normal distribution function of continuous random variable. It was used in a software called ...
1answer
43 views

### T distribution problem

I will be using $t$-distribution to solve this problem. Specifically,the pooled variance test because both samples have size less than $30$,and both populations seem to have the same population ...
0answers
53 views

### Integrating a prob distr over the set of possible circles within an annulus

Let $z$ be the measured coordinates of a point on a circle $c$ with center $x$ and radius $r$. Assume the probability of measuring $z$ given the circle $c$ is normally distributed by the distance ...
2answers
84 views

1answer
96 views

### Derive a hypothesis test Z

Suppose a random sample of size 10 is taken from the random variable X which has the normal distribution with unknown mean $\mu$ and variance 4. You are requested to test the hypothesis $H_0:\mu = 0$ ...
0answers
31 views

### distribution of infinite sum of independent but non-identical normal variables

For $i=1,2,\ldots,n$, suppose $X_i \sim N(0,\Omega_{i})$, where $\Omega_{i}$ is of dimension $k\times k$. It is known that $\frac{1}{\sqrt{n}} \sum_{i=1}^{n} X_i \sim N(0, \overline{\Omega})$, where ...
0answers
50 views

### partical correlation in mixed case binomial and gaussian

For Gaussian mutlivariate distributions it is known, that zero partial correlation corresponds to conditional independence. Is there a same result if one of the variables has a binomial distribution? ...
0answers
111 views

### $\int_{-\infty}^{+\infty}\phi\left(x\right)\Phi\left(\frac{a}{\mathrm{e}^x}\right)dx=\Phi\left(\frac{a}{\sqrt{2}}\right)$

I think I have found a solution to the integral below using similar logic I have found to an answer here http://mathoverflow.net/questions/101469/integration-of-the-product-of-pdf-cdf-of-normal-...
2answers
62 views

### Normal distribution with sample

I'm trying to figure out the best approach to this problem. I would assume that I can use the Central Limit theorem first and then a binomial cdf: Chocolate is packaged into jars using a computerized ...
0answers
36 views

0answers
21 views

### how can we generate random numbers using skew normal distribution

I want to generate random numbers with skew normal distribution using rsn(). I can find the answer from the following link. how can we generate random numbers using skew normal distribution in ...