# Tagged Questions

The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is often used as a reference against which other distributions are compared.

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### Binomial Distribution & t-Test

Starting with a Binomial Distribution with parameters $n=1000, p=0.5$ and measured successes of 300, I would like to test whether there is a significant difference between success and failure. The ...
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### Is it possible to test for a Gaussian distribution?

Suppose that I have $n$ independent samples from a probability distribution. I believe that the distribution is Gaussian ($G$) but I don't know; then my question is: does there exist a test such that ...
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### What is the relationship between the normal and the t-distribution in R (pt and pnorm)?

In R, is it true that: pt(q,df=Inf) $=$ pnorm(q)? Or in words, can I supply df=Inf in ...
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### 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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### Multivariate gaussian log-likelihood

Let's say that we have a 2x5 matrix A where rows correspond to observations and columns correspond to variables from a p-variate Gaussian distribution, and we want to learn the inverse covariance ...
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### How can I make my data fit normal distribution?

I have selected a number of words and asked people to rate them on a Likert scale. Words were selected according to two categories; syllable length (mono-, di- and trisyllable and final phoneme (vowel ...
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### Expected Value of cumulative distribution function

Let $\varepsilon$ be a Gaussian distributed random variable with mean $\mu_0$ and standard deviation $\sigma_0$. Is it possible to compute/approximate the expected value  \begin{eqnarray} & ...
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### why do parametric tests need normal distribution of sample means?

every parametric test has the assumption that the sample means are following a normal distribution. This is the case if the sample itself is normal distributed or if approximately if the sample size ...
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### Confusion related to conditional Gaussian distribution

I have a certain confusion. I refer to this paper. Let's say I have $p$ variables $x_1, x_2, \dots, x_p$ which follow a multivariate Gaussian distribution. Now suppose I have $N$ examples or samples ...
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### How to compute an accuracy measure based on RMSE? Is my large dataset normally distributed?

I have several datasets on the order of thousands of points. The values in each dataset are X,Y,Z referring to a coordinate in space. The Z-value represents a difference in elevation at coordinate ...
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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 ...
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### Likelihood of Conditional Grouped Continuous Model

I would like to find MLE of the likelihood above by using optim function in $R$. However, I couldn't understand the terms. I couldn't write the likelihood in $R$. I have the data given, some of ...
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### RJAGS syntax error using Truncation of normal prior in random effects model [migrated]

I am running a random effects model in rjags with code: ...
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### Estimating parameters of a normal distribution from noisy observation of samples

Suppose I have a number of samples drawn from a normal distribution $x_i \sim \mathcal{N}(\mu,C)$ with $i = 1 \dots n$. I can make observations $z_i = x_i + e_i$ for those samples which are perturbed ...
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### Bivariate Normal distribution and correlation

Is the CDF of a bivariate normal distribution with mean $(0,0)$ and $\Sigma = ((1,\rho),(\rho,1))$ monotone in the correlation coefficient $\rho$?