Tagged Questions

Questions on the Gaussian, or normal probability distribution, which may include multi-dimensional normal distribution.

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Standard Normal Distribution Findng A

I have the following question and i am dumbfounded on how to find the a in my given question. $$\sigma= 10000$$ $$\mu= 50000$$ Find the monthly income which is exceeded by 10 % of employees. I ...
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resource for derivation showing the computing of mutual information for normal random variables

If I have 2 correlated normal random variables, and they are not be jointly normally distributed, is there a closed form answer for their mutual information? I've seen that if two normal random ...
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Probability of being in a circle, given normal

Let's assume a bivariate normal distribution with center $\mu$ and covariance matrix $\Sigma$. Let a circle $C$ be given as $C=\{x\in\mathbb{R}^2:||x-\mu||\leq R\}$. I would like to calculate the ...
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Find the limit of the following series of normal random variables.

Let $X_1,X_2,X_3,…$ be a sequence of i.i.d. $N(\mu,1)$ random variables. Then, find $$\lim_{n\to \infty} \frac{\sqrt{\pi}}{2n}\sum_{i=1}^{n}E(|X_i-\mu|).$$ My thoughts: I don't have any rigorous way ...
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Right way to get groups of data based on amount range

I have a database with about 100K records of invoices (date, provider, type and amount). This is sample data: I want to group my data into 4 segments depending on the amount. Group 1: < X1 ...
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Solve for and Plot the Relationship Between Mean and Standard Deviation of a Normal Distribution Conditional on Satisfaction of A System of Equations

I am trying to use Mathematica, R, or Matlab to solve for (since it cannot seem to be solved analytically) and plot the relationship between mean and standard deviation of a normal distribution ...
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so if I have a normal distribution with z=783 cm and sigma x = 150 cm and sigma y = 50 cm can I scale these sigmas for z=950? if so how? [on hold]

so I have a problem that says if I have a plane at z=783 cm, measure the sigma (standard deviation) of the distribution in the x and y directions. from the graphs projection in the y-axis, projection ...
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norma distribution and log-normal distribution

I often see when people analyzing data, they assume data has either normal or log-normal distribution, and trying to fit data into a distribution for the convenience of data analysis (e.g. by ...
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Show that $(\bar{X})^2$ is not an unbiased estimator for $\mu^2$

If $X_1, ... , X_n$ are $n$ identical distributed independent random variables each with mean $\mu$ and variance $1$. A little confused by this question. Is it asking for if $(\bar{X})^2$ != $\mu^2$....
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How many time the standard deviation, do I need to travel from mean in both directions such that I cover a given percentage of data?

I do not have much experience in Statistics. However, I read this rule on a page and followed it up on Wikipedia: https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule I wanted to know ...
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How to obtain a unimodal histogram with normal distribution (gaussian)?

My task is to come up with a histogram consisting of $N$ bins. The histogram should show a (perfect) normal distribution. So something similar to what is shown in this image. How do I obtain the value ...
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Expectation of absolute random variables with mean 1 and standard deviation 1

For a random variable $\gamma \sim \mathcal{N}(\mu,\sigma)$ , were is $\mathcal{N}$ is the normal distribution. What is the way to calculate the following: $\mathbb{E}[|\gamma|] = ?$ And ...
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What is the chance a team will have at least 10 more wins than losses at any point in a 100 game season? They have a 50% chance of winning each game.

More generally: Each game, $n = 1,2,...,N$, a team has probability, $p = 0.5$, of winning. Their standing $x$ is given by $x(n) = x(n-1)\pm1$ depending on whether they win ($+1$) or lose ($-1$). Their ...
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I need help normalizing a Gaussian kernel matrix to integer values

I am trying to understand the mathematics behind Canny edge detection, and the first step is to apply a Gaussian blur to the image you are working with. To do a Gaussian blur, you must obtain a ...
Suppose I have a complex random variable $X$ which follows a complex normal distribution (with $0$ mean). I've been trying to represent the complex normal in a simpler way, but I'm not sure how. Is ...