# Questions tagged [normal-distribution]

The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality] tag for asking about testing for normality.

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### How to develop a model in R to illustrate that sum of two variables normally distributed if these two variables each follow a Normal distribution?

I was wondering how can I use code in R to set up a simulation to show that if two random variables each follow a normal distribution with given means and variances, their sum is also normally ...
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I am trying to simulate a list of transactions of the type that would appear on the bank statement, eg ATM visits rent/food payments, salary deposit, etc. For generating random transactions the focus ...
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### Distribution of $\frac{1}{X}$ if $X\sim N(0,1)$

Given a random variable $X$ that has a normal ditribution with mean $\mu$ and standard deviation $\sigma$, what is the distribution of $\frac{1}{X}$? I guess that it like a normal distribution ...
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### How close a sample is to the Normal distribution ( Berry-Esseen Theorem)

My question is how can I use the Berry-Esseen Theorem to know how close to the Gaussian distribution is $L$, where $$L=nLn(2)+Ln(r_1)+Ln(r_2)...Ln(r_n).$$ $r_i \geq 0$ is a i.i.d. random variable ...
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### characterization of circularly symmetric complex Gaussian variable

Let $Z=X + jY$ be a complex random variable, where $X$ and $Y$ are real. By definition, $Z$ is said to be circularly symmetric complex Gaussian $\mathcal{CN}(0, \sigma^2)$ if $X$ and $Y$ are ...
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### What a normal curve actually is?

I am fairly new to Stats and thus this question. I was going through different materials to learn stats. Somewhere it's mentioned that a population, if plotted against frequency on a bar graph can ...
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### Probability that one Normal RV is greater than at least one of a set of other Normal RVs

For a side project I am working on I need to find the probability that a given Normal rv from $N(\mu_a,\sigma_a^2)$ is greater than or equal to at least one of the values from a set of other, unique, ...
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### The second order moments of the Gaussian multivariate distribution

I am really quite confused to how to calculate and get the result from to I know the symmetry will recduce the sum of j to sum of i(yiyj to yiyi),but however, it is still difficult for me to think ...
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### Expected value of the exponential of a normal CDF

Let $x$ be distributed according to a standard normal. Let $\Phi(y)$ denote the cumulative distribution function of a standard normal evaluated at $y$. Let $a$ and $b$ be real scalars. It is easy to ...
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### NaiveBayes: Adding a new predictor which is random noise

In the NaiveBayes method, can adding a random noise vector where each element is sampled from, e.g., a standard normal distribution, help? In what cases this may be a 'clever' approach? I imagine ...