Tagged Questions

69 views

Finding the mean of a Gaussian distributed random variable given the variance

I have a Gaussian distributed random variable $X$ with known variance $\sigma^2$. Given that I know $P(X\geq t)=m$, how can I find the mean of the random variable?
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Approximation of the variance of the first order statistic (min) of normal random variates

I'm looking for a closed form approximation of the variance of the minimum order statistic for normal random variates. Can anyone point me to a reference, or an approximation? I've seen the post ...
57 views

Standard error from correlation coefficient

Many studies only report the relationship between two variables (e.g. linear or logistic equation), $n$, and $r^2$. I want to use these reported statistics to reproduce this relationship with its ...
64 views

How to combine variances from sensors where each observation has its own variance?

I have a set of measurements $x_1$ ... $x_n$. These measurements are normally distributed, measuring the same value. However due to the way the data is measured, each $x$ has its own standard ...
77 views

193 views

Distribution which has maximum or minimum variance for a given entropy

We know that the normal distribution has the maximum entropy among all continuous distribution on $\mathbb{R}$ for a given variance. I wonder what's the opposite, i.e. what distribution has the ...
520 views

Confidence Interval for variance given one observation

This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory": Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters ...
96 views

Monomial distribution of $X^a \cdot Y^b$

What is the distribution of the following monomial? $$X^a \cdot Y^b$$ where $X$ and $Y$ are normal random variables and $a$ and $b$ are natural numbers. For example, when $X \sim N(0,1)$, $a=2$, and ...
385 views

Are logistic regression coefficient estimates biased when the predictor has large variance?

I'm simulating data from a logistic regression model: log(p/1-p)= 0 + X where $X \sim N(0,\sigma^2)$. After I simulate the data, I fit a logistic regression ...
1k views

Why is the variance of $X-Y$ equal to the sum of the variances when $X,Y$ are independent?

I have one question about this. I know that if we have $\mathrm{X}_1,\mathrm{X}_2,\ldots,\mathrm{X}_n$ independent and normally distributed random variables, then the sum ...
135 views

Is 2-sigma limit applicable as a measure of variance to a distribution?

There is a paper that uses something like the 2-sigma limit to check if a quantity is more-or-less constant. More specifically in this paper on Text Detection (Sec. 3.2 3rd para last line) this limit ...
758 views

Mean of a product of Gaussians

If I have two normally distributed random variables, X and Y, and I want to find the mean of the distribution that results from multiplying them together, which of the following two formulas should I ...
605 views

Is the variance of the multivariate folded normal distribution known?

The mean and variance of the folded normal distribution are known. Consider now the distribution of $(|x_1|, \ldots, |x_n|)$, where $\mathbb{x} \sim N(\mu, \Sigma)$. The mean of the multivariate ...
708 views

How to deal with a non-gaussian distribution & heteroscedasticity

I am working on my thesis project and have come across a problem with the statistics which I am looking for a bit of guidance. I am running ANOVA tests to determine significance between groups but i ...
188 views

How does number of observations supporting alternate hypothesis on a test of a variance have to scale so that null is rejected?

Informal explanation: In the course of my research I've run into the following problem: I am observing a machine that outputs random numbers. Most (if not all) of these random numbers come from the ...
539 views

Is my data distribution normal? (Tried Shapiro and Kolmogornov-Smirnov tests)

I have a 1D data set with 83163 data points, and I would like to know whether the data follows a normal distribution. I tried using shapiro.test and ks.test in R: d is a vector containing the data ...
301 views

Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers

An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
483 views

What is the variance of the sum of components of a multivariate normal distribution?

I'm talking with my advisor about how to compute standard deviations for, say, combined standardized test scores for admissions purposes. For example, we'd be interested to compute the sum of the ...
264 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. ...
895 views

When estimating variance, why do unbiased estimators divide by n-1 yet maximum likelihood estimates divide by n?

I am totally confused: On the one hand you can read all kinds of explanations why you have to divide by n-1 to get an unbiased estimator for the (unknown) population variance (degrees of freedom, not ...
166 views

Inference with Gaussian Random Variable

Let $X = N(0,\frac{1}{\alpha})$, $Y = 2X + 8 + N_{y}$, and $N_{y}$ be a noise $N_{y} = N(0,1)$. Then, $P(y|x) = \frac{1}{\sqrt{2\pi}}exp\{ -\frac{1}{2}(y - 2x - 8)^{2} \}$ and \$P(x) = ...