# Tagged Questions

113 views

### Compute sum of vectors drawn from multivariate normal, subject to a linear constraint

I want to compute $S = \sum_{i=1}^n x_i$ where $w^t x_i>-1, \; \forall i$ and $x_i \tilde{} \mathcal{N}(\mu, \Sigma)$ for known $w$, $\mu$ and $\Sigma$. I know $S$ can be approximated by sampling ...
204 views

### The sample size applied to a non-normal distribution

I have a single variable that represents my population values (sample of data): ...
135 views

### How do I sample multiple normally distributed items and maintain a fixed sum?

Suppose jars are being filled with Red, Green and Blue balls in an approximately fixed ratio. The total number of balls that fits in a jar is fixed (say N=1000). I know the mean and standard deviation ...
237 views

### Normal distributed random numbers in time - expected behaviour - askew distributions?

I have a 3D array of numbers, initialised with normal distributed values. The mean of the distribution is $0$, the standard deviation in the order of $10^{-5}$ to $10^{-8}$, but would be constant for ...
105 views

### Computing conditional expectation of ordered normal random variables

There are $m$ normally distributed, independent random variables $N_1, \ldots, N_m$ with distinct means $\mu_1, \ldots \mu_m$ and standard deviations $\sigma_1, \ldots, \sigma_m$. Then, we observe a ...
5k views

### How does the sampling distribution of sample means approximate the population mean?

I am trying to learn statistics because I find that it is so prevalent that it prohibits me from learning some things if I don't understand it properly. I am having trouble understanding this notion ...
218 views

### Distribution of ratio of sample means from two independent normal variables?

The Question We have a sample of size $N$ with mean $\bar{x}$ and SD $\bar{\sigma_x}$ from a random variable $X \sim \mathcal{N} (\mu, \sigma^2)$ We have a sample of size $M$ with mean $\bar{y}$ and ...
55 views

### How to pick from a set of random variables the one with the highest mean using a fixed number measurements?

Suppose we have $N$ approximately normally distributed continuous random variables $X_1, X_2, X_3, \ldots,X_N$, each with an unknown mean and variance. I'd like to find the random variable with the ...
222 views

### Gaussian Like distribution with higher order moments

For the Gaussian distribution with unknown mean and variance, the sufficient statistics in the standard exponential family form is $T(x)=(x,x^2)$. I have a distribution that has ...
330 views

### Is this an unbiased estimator for standard deviation of normal distribution?

Suppose we have $n$ samples, with mean $\mu$. Calculate the average absolute distance from $\mu$, i.e., $$y = \frac{1}{n} \sum_{i=1}^n |X_i - \mu| \>.$$ Then, take as an estimate of the ...
1k views

### How can I calculate cut-off points from a normal distribution?

I'm trying to calculate the upper percentage points for the 0.99 percentile for samples drawn from a normal distribution, with a sample size of 500. How can I calculate the expected values for ...
323 views

### What are the sampling distributions of higher moments of the normal distribution?

Let $X_i$ be independent, normally distributed random variables, for $1\leq i\leq N$. What is the distribution of $Y_m=\frac1 N \sum_{i=1}^N X_i^m$? Every high school student knows part of the ...
6k views

### How to sample from a normal distribution with known mean and variance using a conventional programming language?

I've never had a course in statistics, so I hope I'm asking in the right place here. Suppose I have only two data describing a normal distribution: the mean $\mu$ and variance $\sigma^2$. I want to ...