# Tagged Questions

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

167 views

### Are there order statistics for a Gaussian variable raised to a power?

Let $X$ be a random variable with a standard normal distribution. Let $Y = |X|^{2p}$. I am trying to find the distribution for $Y_{(n)}$, i.e., the largest value of $Y$ out of $n$ samples. I have ...
41 views

### Explaining the standard deviation formula

I'm revisiting standard deviation for the first time years, and i can't for the life of me recall the difference between two formulas. In particular, im also looking for how we arrived at these ...
31 views

### Calculating transformation of normal random variables.

Let's say you have 4 i.i.d $N(0, 1)$ random variables $X_1 ,X_2, X_3, X_4$, how would you compute the pdf of $\frac{X_1}{\sqrt{X_1^2 + X_2^2 + X_3^2 + X_4^2}}$. I am also interested in the general ...
36 views

### Finding the normal distribution using excel

Let's say the lifetimes of a set of tires is normally distributed with a mean of 65,000km and a standard deviation of 6,500km. If a random sample of 9 of the new type of tire are tested, what is the ...
83 views

37 views

### Product of (dependant) gaussian distributions

I need to find the probability of sampling a specific point on a Gaussian Distribution. The catch is that the mean of the first Gaussian Distribution is itself sampled from a Gaussian Distribution. ...
24 views

### Marginilizing in multivariate Statistical Distributions

Suppose we draw $X = [x_1,...,x_i,...x_r,...,x_t...,x_j,...x_N]$ from $N(0,\Sigma)$. is there any way to compute $E[x_ix_j]$ and how about $E[x_ix_jx_rx_t]$ ? How can I compute the marginal ...
35 views

### Joint Density and Covariance between Two Random Variables with the same Mean and Variance

This seems like a deceptively simple question, (and it perhaps is and I am missing something) but I could not find anything on this. Q1) Are there any general results / relationships to get the ...
65 views

### Simple question on conditional probabilities (multidimensional normal distributions)

Let $X$ and $Y$ in $\Bbb{R}^n$ be two random vectors. We assume that $X\mid Y\sim\mathcal{N}(Y,\Sigma_X)$ and $Y\sim\mathcal{N}(\mu_Y,\Sigma_Y)$ The goal is to sample from the distribution of $X$. ...
16 views

### Length of Multinormal Distribution

Let $X \in R^n$ be a random normally distributed vector with $E X = \mu$ and $\text{Var } X = \Sigma$. Is there a neat way to calculate the variation of $|X|$, the length of $X$? I know how to ...
16 views

25 views

### on a quantisation of the bell curve

The bell curve function: $e^{-x^2/2}$ is an eigenfunction of the Fourier transform (FT) on the real line. Is its quantisation/discretisation the binomial distribution (coefficients $n$ choose $k$) an ...
I am wonder how to standardize multivariate normal value. Normal standard multivariate distribution of $q$ variables is $z\sim N_q(0_q,I_q)$. I have found that $Bx\sim N_q(Ba,B\Sigma B^T)$ and based ...
Using the central limit theorem, I was able to find out the first part of this question. However, part b is eluding me. How do I, in general, find a value for $n$ such that we can ensure the ...