Tagged Questions

3
votes
1answer
60 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 ...
2
votes
1answer
65 views

The sample size applied to a non-normal distribution

I have a single variable that represents my population values (sample of data): ...
0
votes
1answer
54 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 ...
5
votes
1answer
193 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 ...
1
vote
1answer
82 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 ...
2
votes
3answers
2k 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 somethings if I don't understand it properly. I am having trouble understanding this notion of ...
5
votes
2answers
161 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 ...
4
votes
0answers
50 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 ...
6
votes
0answers
168 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 ...
3
votes
0answers
254 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 ...
1
vote
1answer
861 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 ...
2
votes
1answer
249 views

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

Let Xi be independent, normally distributed random variables, for 1≤i≤N. What is the distribution of Ym=N-1Σ(Xi)m? Every high school student knows part of the answer. The mean of Ym is ...
10
votes
5answers
4k 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 ...
2
votes
1answer
600 views

Some exercises related to sampling and the normal distribution

Following cardiac surgery, patients are encouraged to exercise regularly (assume that regular exercise is defined as exercising on 3 or more days per week). A physician suspects that patients exercise ...
6
votes
1answer
228 views

Estimating the variance of poker win rates

Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. ...