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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18 views

I did this problem but I got percents as the answer not two values. What did I do wrong?

Suppose that the lifetime of a particular electronic circuit has a normal distribution with mean of 50,000 hours and a standard deviation of 8,000 hours. You select a random sample of 25 circuits 1) ...
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0answers
22 views

sum of truncated normal with two normal distributions

Suppose I have one normal distribution $W \sim N(\mu_{x},\sigma_{w})$ with a known cuttoff point (percentile) on this distribution called c. The first part of $W \in [-\infty,c[$ needs to be ...
5
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0answers
59 views

What Ratio of Independent Distributions gives a Normal Distribution?

The ratio of two independent normal distributions give a Cauchy distribution. The t-distribution is a normal distribution divided by an independent chi-squared distribution. The ratio of two ...
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0answers
11 views

Folded Normal and truncate Normal

Suppose to have a vector of random variables $\mathbf{y}$, distributed as a multivariate normal with mean vector $\boldsymbol{\mu}$ and covariance matrix $\boldsymbol{\Sigma}$. The variable ...
4
votes
1answer
67 views

Why is the sampling distribution of variance a chi-squared distribution?

The statement The sampling distribution of the sample variance is a chi-squared distribution with degree of freedom equals to $n-1$, where $n$ is the sample size (given that the random variable of ...
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0answers
9 views

How do I determine sample size to validate a requirement when I have a lot of margin?

I apologize if a similar question has been asked, but my search has yielded no results. I am having some trouble nailing down the correct methodology to use to design an experiment I am working on. ...
2
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2answers
63 views

What characteristics should a distribution have for CLT to work?

If a "distribution" is constant, then CLT is not going to work, obviously. However, even if it is not a constant, but variance is very small, the distribution of the sums is still not normal. For ...
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24 views

Two Gaussian Likelihoods with Two Decision Boundaries , 0/1 loss function

we assume that Y := {1, 2}. Then our decision can be re-written as y ∗ = {1 if p(x|y = 1) > p(x|y = 2) , 2 otherwise} with a decision boundary at p(x|y = 1) = p(x|y = 2). How can we construct an ...
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1answer
27 views

Distribution of random sample of confidence intervals containing the true mean

Given 50 random samples, each of size 25, from a normal distribution with mean 20 and standard deviation 5. From each of the 50 samples, you can find a 90% confidence interval for the mean. Let Y be a ...
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0answers
44 views

Best way to determine normality of data

I believe there are many ways to determine if data is normal or not: histogram shape QQ plot skewness kurtosis shapiro test. Which of the above is the best way to determine if data is normal and ...
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0answers
18 views

Cannot intuitively grasp “Standard normal deviate”

I cannot intuitively grasp the meaning of "Standard normal deviates". I think It would help if you provided me with either/all of the following: (i) real life examples of their application, (ii) an ...
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0answers
20 views

How to calculate distribution of Y|X from distributions of X|Y and Y [duplicate]

I'm trying to solve the following homework problem: Let $X$ given $Y=y$ have a normal distribution with mean $y$ and variance one, and let the marginal distribution of $Y$ be normal with mean ...
3
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1answer
102 views

Example of two *correlated* normal variables whose sum is not normal

I am aware of some nice examples of pairs of correlated random variables which are marginally normal but not jointly normal. See this answer by Dilip Sarwate, and this one by Cardinal. I am also ...
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1answer
18 views

Bayesian calculation of parameter multiplying normal

I am interested in a model like: $y_{i} = \sum_{k\in K}{\beta_{k} z_{k}}$, with $z_{k} \tilde{} N(\mu_{k}, \sigma_{k})$. where $\beta \equiv(\beta_{k})_{k\in K}$ is not known, but all else is. I ...
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0answers
29 views

Independence of functions of Random variables [closed]

I am working with two RV's X and Y X is distributed normally with mean=x and variance=x^2 Y is distributed uniform (0,1) I know this... ...
6
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1answer
411 views

Why should we use t errors instead of normal errors?

In this blog post by Andrew Gelman, there is the following passage: The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian ...
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0answers
66 views

Normal Distribution with mean and standard deviation

I'm trying to solve the following problem: Suppose at breast height, the diameter of trees of a particular type is normally distributed with mean=8.8 inches and standard deviation= 2.8 inches.What ...
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1answer
35 views

Calculating the expected value and variance of an estimator of a normal quantile

I don't quite understand how to use the estimator function and the variance function and plug in the sample mean. I expected that we would plug in the value $\bar X - 1.645s$ into $E(s)$ and $V(s)$. ...
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1answer
39 views

How to make a vertical line in R [closed]

curve(dnorm(x,90,10),from=60, to=120) I need to make some vertical line in the x line that in number 70 and 110. How should I do it?
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0answers
22 views

Find the Distribution of a Function of a Multivariate Normal

I'm having trouble with the following question. Suppose $X \sim N(\mu, \Sigma)$, where $\mu \in \mathbb{R}^k$. Let $Y= AX +b$, where $A$ is an $n \times k$ matrix of constants and $b$ is an $n$ ...
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0answers
35 views

Clarification on Central Limit Theorem [duplicate]

I have this (some_variable, frequency) data. Initially when I plotted the top 10% of this list. I got below, graph (zipf's graph) - Now with this data, I ...
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0answers
19 views

Distribution of noninjective function of random variables

Let $(X,Y)$ is a bivariate normal random variable wit mean $(0,0)$ and covariance matrix $\Sigma.$ Suppose that $T:\mathbb R^2\mapsto\mathbb R.$ I wish to compute the distribution of $T(X,Y).$ How ...
3
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1answer
46 views

Convert Poisson distribution to normal distribution

I primarily have a computer science background but now I am trying to teach myself basic stats. I have some data which I think has a Poisson distribution I have two questions: Is this a Poisson ...
0
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1answer
19 views

Finding $p(\tilde{y}|x)$ given measurement model and error distribution

Given two measurements of a variable $x$: $\tilde{y_1}=x+e_1$ $\tilde{y_2}=x+e_2$ where $e_1,e_2$ are zero-mean random variables following a bivariate normal distribution, with a known joint ...
3
votes
2answers
164 views

What causes non-normality of the error term in OLS?

In data, what causes the error term to be non-normally distributed in regression? Along the same lines, what solutions are there for non-normal residuals? For example, is it caused solely by a ...
1
vote
1answer
59 views

Estimation based on observing sum of two variables

Let $X_1,\dots,X_n$ are i.i.d normal $N(\mu,\sigma^2).$ Suppose that we only observe $$ X_1+X_2,\dots,X_1+X_n,\dots,X_{n-1}+X_n, $$ i.e, $X_i+X_j$ for all $i<j.$ I wish to find the best estimator ...
0
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1answer
33 views

Help interpret Distribution of Wlan Signal Strength Measurements

For my project I need to evaluate large amounts of wlan signal strength measurements. Measurement is in dBm which is a logarithmic scale for milli watt (so every 3dBm the milliwatts double) where ...
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0answers
27 views

Distance between two independent normal random variable

What is the PDF of $Z=\sqrt{(X-x_0)^2+(Y-y_0)^2}$ when X and y are i.i.d. zero mean normal random variable (i.e., $x\sim N(0,\sigma^2)$ and $x\sim N(0,\sigma^2)$)
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1answer
30 views

Finding the probability that a set of measurement belongs to a set of normal distributions

Suppose that we are given a set of $n \cdot k $ normal distributions so that a given measurement of $k$ values either comes from a given set of $k$ normal distributions or not. How do we calculate the ...
1
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0answers
31 views

Estimating of variance of dependent normal distribution

Let $X_1,\dots,X_n$ are independent and identically unobservable variable on $\Omega$. Suppose that $f:\Omega\times\Omega\mapsto \mathbb R$ be unknown function such that we know the value of ...
4
votes
1answer
28 views

Most probable value given observation

Suppose I have observed $Z = 3$, where $Z = X + Y$, where $X \sim N(0,9), Y \sim N(0,4)$. How would I find the most probable value of $X$ that would have given me $Z = 3$? My attempt at a solution: ...
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0answers
29 views

Quad precision normal cdf and quantile functions

I'm looking to run the normal distribution cumulative distribution function and quantile function (its inverse) using the quadruple precision floating point format. Does anyone know of a library that ...
1
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1answer
49 views

Constrained MLE of multivariate normal

this might be obvious one but I have spent much time without gaining anything. If $\underline{X}$~$N_p(\underline{\mu},\sigma^2 I)$, where $\mu$ is known to lie on the unit sphere ($\mu^T\mu$), show ...
3
votes
2answers
63 views

Correlation estimation on Half-Normal Distribution

Let $$(X,Y)\sim N\left(\begin{pmatrix}0\\0\end{pmatrix},\begin{pmatrix}1&\rho\\\rho&1\end{pmatrix}\right)$$ and let we are observing $(|X_1|,|Y_1|),\dots,(|X_n|,|Y_n|)$ independently. I wish ...
3
votes
1answer
92 views

What is the median of an equally weighted mixture of two Normal Distributions?

Suppose men's heights follow a normal distribution $X \sim \mathcal{N}(\mu_1,\sigma_1^2)$ and women's heights follow a normal distribution $Y \sim \mathcal{N}(\mu_2,\sigma_2^2)$. How can I find the ...
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0answers
17 views

When do we “bootstrap” and then use “t-dist” versus just using “t-dist”?

I'm taking a Data Analysis class on Coursera, and we are learning about bootstrapping when you have a small sample size (>30). What I don't understand, is when do you bootstrap and then use the ...
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2answers
373 views

Simulating draws from a Uniform Distribution using draws from a Normal Distribution

I recently purchased a data science interview resource in which one of the probability questions was as follows: Given draws from a normal distribution with known parameters, how can you simulate ...
0
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1answer
64 views

R code to solve for probability of normal distributions?

I don't understand which R code I am supposed to be using to figure these problems out. I brief explanation of what the code is doing would be amazing. The problems below are two different ...
1
vote
1answer
22 views

Back transformation with power function

I have the following distribution, where each observation represents a metric. $Metric = \frac{NExplored Nodes \times NGenerated Nodes}{NRepeated Nodes}$ This metric is highly correlated (0.99637) ...
0
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0answers
31 views

How do I use R code to solve for probability of normal distributions? [duplicate]

I don't understand which R code I am supposed to be using to figure these problems out. I brief explanation of what the code is doing would be amazing. The problems below are two different ...
0
votes
0answers
18 views

Linear Combination of Random Normal Variables

In order to prove that the linear combination of two independent normal distributions(say Z=X+Y) is normal, i am using their MGFs to show that the linear combination also has a similar mgf. This works ...
2
votes
2answers
118 views

Mean value of truncated normal distribution

I have a bunch of data where each observation represents an error $\in [0,1]$ (computed error between a variable and it's ground truth). Extra info: These are the results of the difference between a ...
2
votes
1answer
20 views

Percentage Beyond a Given Value for Empirically Defined Distribution

It is my understanding that standard deviation does not work well as a measurement for distributions that are heavily skewed. If I have a heavily right-skewed distribution, should I simply use the ...
1
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1answer
30 views

Why constrain mean and standard deviation when proving Gaussian is maximum differential entropy pdf?

I'm reading Bishop's Pattern Recognition and Machine Learning. In chapter 1.6: Information Theory (page 53) when trying to derive the maximum differential entropy pdf from the definition of continuous ...
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2answers
168 views

Why do we have to assume normality for a one-sample t-test?

As a consequence of the central limit theorem the sampling distribution of the sample means will always be normal whatever is the distribution of the variable we measure. From our sample we can ...
3
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1answer
35 views

degenerate univariate Gaussian

I was watching a video on Gaussian distributions and it defined the degenerate univariate Gaussian as a Gaussian where the variance is zero. However, I am really struggling to understand how the ...
0
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1answer
65 views

How do I use the Hessian matrix for maximum likelihood estimation?

I am trying to teach myself maximum likelihood estimation using the Newton-Raphson method and related iterative methods. I don't understand the link between the hessian, the expected value of the ...
0
votes
1answer
33 views

Variance and asymmetry on relative frequency class distribution

I don't know how to resolve this (easy) exercise. I've calculated the first output. But I don't know if it's correct. Calculate arithmetic mean, variance (standard deviation^2), concentration and ...
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0answers
34 views

Estimate the covariance matrix of a normal distribution if the mean vectors is given by a linear rule

Let $X=(x_1,\ldots,x_n)^\top\in\Bbb{R}^n$ be a random vector that follows a multivariate Gaussian distribution with known mean vector $\mu=(\mu_1,\ldots,\mu_n)^\top\in\Bbb{R}^n$. The covariance matrix ...
2
votes
1answer
58 views

Analyzing the effect of categorical variables on a correlation coefficient

For my research project, I’m looking for some help on how to analyze my data. The research setup is as follows: I’ve got two normal variables that I want to correlate with each other and a number of ...