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

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0
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1answer
18 views

Slow convergence simulating log-normal sample from the normal

I am trying to simulate a log-normal random variable $Y$ with mean $m = \mathbb{E}[Y] = 0.001$ and standard deviation $s = 0.094$ by simulating a normal sample instead, and then exponentiating it. ...
1
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0answers
15 views

Sum of two independent truncated gaussians

I'd like to ask for additional info regarding a previous post on the subject: Sum of two truncated gaussian but I can't comment directly on that. Assume $X \sim N(\mu_{1}, \sigma_1^2)$ is doubly ...
1
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0answers
35 views

Find a probability density

I am going through a paper trying to understand all the single steps, but I got stuck. I need to calculate $$p(x+\delta t) \mid x(t), t)= \int p(x(t+\delta t) \mid \mu , x(t), t)p(\mu\mid x(t), t) ...
0
votes
1answer
8 views

How do I solve this question using Z Table and Normal distribution?

A company pays its employees an average wage of 15.90 an hour with a standard deviation of 1.50. Assume the wages are approximately normally distributed. a) what proportion of employees receive ...
5
votes
2answers
267 views

Triangular vs Normal distribution

I'm trying to approximate a standard normal distribution with a triangular distribution. What parameters of the triangular distribution (min, max and mode) are more suitable? Thank you
1
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2answers
29 views

Variance of |X-Y| for X and Y ~ N(0,1/2)

I know $X$ and $Y\sim\mathcal{N}(0,\frac12)$, $X$ and $Y$ are independent. I try the following way to solve variance of $g(X,Y)=|X-Y|$ ,which is $V(|X-Y|)$. If ...
0
votes
1answer
20 views

Type I error in Normal distributions

Let $X_1,\dots , X_n \stackrel{iid}{\sim} N(\mu, \sigma^2 = 4)$ Test $H_0: \mu = 10$ vs $H_1: \mu > 10$ take a random sample of $n=16$ and reject $H_0$ if $\bar{x}>14$ Find $\alpha$ the type I ...
2
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0answers
33 views

Help Integrating $I=\int\Phi\left(\frac{p}{\sqrt{q+rx}}\right)dx$

I am trying to integrate the following function involving the Normal CDF ($\Phi$). I actually need the definite integral $$\int^b_a\Phi\left(\frac{p}{\sqrt{q+rx}}\right)dx$$ for $q+ra,q+rb >0$ but ...
0
votes
1answer
34 views

Sum of two truncated normaly distributed variables

Let $X$ and $Y$ be two variables which are truncated normally distributed above zero (that is $X$ and $Y$ have the lower truncation point zero, their values are bounded above zero). Is $X+Y$ truncated ...
0
votes
1answer
22 views

Probability with intersecting normal distributions

There are two independent random variables $a$ and $b$, each distributed normally with their own parameters. Given the means and standard deviations for $a$ and $b$, how can I calculate $P(a < b)$? ...
-3
votes
0answers
21 views

Normal Distribution Table urgent help [on hold]

I have been asked to find this, $ P(−2 ≤ Z ≤ 2).$ I need to know how to find this, don't understand the last step when you add $0.5.$
2
votes
0answers
24 views

One-sided Bound on Sum of Fourth Moments

I'm interested in methods for proving one-sided bounds of the form $$ \mathbb{P}[\frac{1}{n}\sum_{i=1}^n X^4_i \geq 3+t]\leq Ce^{-nt} $$ where $X_i$ are standard normal random variables. I've run a ...
0
votes
1answer
19 views

Confidence Interval w/ true standard deviation?

I'm very scared that my calculations I did were wrong. Here is why: I assumed true standard deviation meant population S.D. However the question says the standard deviation is from a sample. So what ...
0
votes
1answer
11 views

Normal Distribution $r-1$ th moment with absolute value

I was stuck for this problem whole night and I tried numerical solution using MATLAB and the following result seems hold for x follow normal N(0,1) and for any positive number (not integer only) ...
1
vote
2answers
24 views

How to I use the standard normal table to get the following Z value?

So I am given that $P(X \le 31.5) = 0.05$ and according to the textbook, after standardizing and using the standard normal table we get $$(31.5 - \text{mean})/(\text{standard deviation}) = ...
1
vote
0answers
23 views

mean and variance of this Gaussian random variable

I am trying to read through this paper - http://www.malcolmdshuster.com/Pub_2002c_J_scale_scan.pdf Equation 2(b)from the paper says [A] $\nu_k \equiv 2(B_k - b).\epsilon_k - |\epsilon_k|^2 $ where ...
0
votes
1answer
40 views

Combining normal distrubutions

I am not sure of the terminology here, if this is a product, summation, or average. How can you take a two unimodal normal distributions and combine them into a bimodal distribution? And then combine ...
1
vote
2answers
34 views

Ratio of CDF to PDF increasing?

Let $\Phi(x)$ be a cumulative normal distribution function and $\phi(x)$ the associated probability density function. Is the ratio $\frac{\Phi(x)}{\phi(x)}$ increasing in x? Numerically it seems to ...
3
votes
1answer
23 views

A tool weight is distributed normally with mean = $2265.4$. Given that 14% of the tools' weight are above 2278.36. what is the standard deviation?

A tool weight is distributed normally with mean = $2265.4$. Given that 14% of the tools' weight are above 2278.36. what is the standard deviation? Here the solution: denote $X$ as tool's ...
0
votes
0answers
30 views

Perturbed density of eigen-states of a 3 diagonal matrix

How does the density of eigen-states ($D(\lambda)$ is defined as $D(\lambda) d\lambda$ = Number of states in the range $\lambda ... \lambda + d\lambda$) of the following tridiagonal matrix ($A$) ...
0
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0answers
23 views

Distribution of Difference of Ordered Values Drawn From A Normal Distribution

This question has come up at least twice now when I was trying to estimate something*. I could always write out the integral or find it computationally but I'm hoping someone will give me an exact ...
0
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0answers
24 views

How to distribute a cost in a normal distribution

I need to spread out a number so that it reflects a normal distribution. For example, I have an item that cost $500,000$ dollars in year $2050$ and I would like to spread it across with a standard ...
0
votes
1answer
41 views

Normal distribution, $S^2$ distribution, and chi-square distribution exercise

Let $X_1,\dots , X_{16}$ be a random sample from a normal population with mean $\mu= 6$ and variance $\sigma^2 = 4$. (a) What is the approximate distribution of X? (b) Find $P( X< 4)$ (c) Find ...
1
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1answer
32 views

Normal Distribution Approximations and Central Limit Theorem

Let $X_1,\ldots,X_{144}$ be a random sample from a population with mean $\mu = 20$ and variance $\sigma^2 = 64$. (a) What is the approximate distribution of $\bar X$? (b) Find $P( \bar{X} < ...
0
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0answers
13 views

Relation between camera megapixels and signal to noise ratio

Disclaimer: I understand that this thing does almost nothing to photography (as noise is not so important to photography is self and because there are a lot of things influent to signal to noise like ...
0
votes
1answer
38 views

Calculate multivariate Gaussian from univariate Gaussian

I am currently trying to solve an exercise that involves estimating the position $\chi_t$ and and velocity $\dot\chi_t$ of a truck at time $t$. The truck moves on rails and is buffeted around by a ...
0
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0answers
32 views

For any $p$ we have $f\in D(\mathbb{R})$

Let $\varphi\in D(\mathbb{R})$ and $f=\varphi+p$ , $p$ is polynome $\star$ For any $p$ we have $f\in D(\mathbb{R})$ ?
1
vote
1answer
22 views

Normal Distribution Quartiles

lets say the first quartile of a random variable (continuous one) has a CDF function F such that $F(x) = .25$... e.g. the random variable is $3\times$ as likely to be larger than the first quartile ...
0
votes
1answer
22 views

Normalizing relative list of probabilities

I have an array of objects, and I want to randomly select one. These objects all have a performance property that ranges between [0, 1]. If this performance value is greater than (or equal to) some ...
0
votes
0answers
27 views

Converting normally distributed numbers to uniform distribution

I have a Perlin noise algorithm I've written my self. It seems to produce gausian numbers at the range of -1.5 and 1.5 but I'll convert them to the range of -1 and 1. I' currently working on a project ...
2
votes
0answers
43 views

Uniform convergence of functions involving normal CDF

Consider two sequences of continuous functions $(f_n)$ and $(g_n)$ for $n \geq 0$ defined by $$ f_n (x) := \int_0 ^t \Phi\left(\frac{x\Phi ^{-1}(\alpha(s) + \beta_n(s))+\Phi^{-1} ...
0
votes
1answer
29 views

What is the distribution of the sum of several normally distributed random variables?

Let's say we have n normally distributed random variables all with the same median and variance. Do we have a possibility to estimate the distribution law of the sum of those variables? I assume ...
-1
votes
0answers
26 views

Normal distribution with unknown mean and variance

I've just done 3 pages of algebra having a go at this before realising I made a stupid mistake right at the beginning so it's all wrong. Moreover, I'm not sure my method was right (see below). I have ...
0
votes
0answers
41 views

Mean, variance and normal distribution

In a game of bridge hands of size 13 are dealt to each of 4 players in such a way that each hand can be considered to be a random sample without replacement from a standard pack of 52 cards. Each ...
1
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0answers
21 views

Coupling a chi-square to a normal random variable

Let $Z\sim \chi^2(k)$ be a random variable sampled from the Chi-Squared distribution with $k$ degrees of freedom. Vague question: Conditional on the value of $Z$, how can I reconstruct a sequence of ...
1
vote
1answer
17 views

Confidence ellipse for a 2D gaussian

For a 1D gaussian, the interval +/- 1SD about the mean will comprise ~68% of the area under the curve. Consider a 2D gaussian with a mean of zero and a diagonal covariance matrix (i.e., it is not ...
0
votes
1answer
11 views

The value of z representing the first Quartile of the standard normal distribution is:

I'm in desperate need of a hint at how they got the answer.
0
votes
1answer
29 views

Normal Approximation to the Binomial (Multiple Choice Question)

My first instinct in this question is use Normal approximation because N is large, and P is exactly between 1 and 0. I used the normal approximation, calculated when $p(X\le 19)$ and got 0.8997. The ...
0
votes
4answers
59 views

If $X \sim N(\mu, \sigma ^2)$, show that $(X - \mu) / \sigma \sim N(0,1)$ [closed]

I don't know how to do this. Do I need to use converge in distribution? (I thought this can only been used if $n$ involves)
1
vote
1answer
19 views

Argument shift Normal Distribution

In a mathematic book I have read following exercise: We throw a normal coin 10,000 times. The random variable $X$ tells us the number of tails. Give an approximation for $\mathbb{P}(4900 \leq X ...
2
votes
0answers
42 views

what is the expectation of $\sqrt{\left | x \right |} * sign(x)$ and $log(|x|)$ for a normal distribution

(1) What would $\int_{-\infty }^{\infty} \frac{\sqrt{\left | x \right |} * sign(x)}{\sqrt{2\pi}\sigma}e^{-0.5*\left ( \frac{x-\mu}{\sigma} \right )^{2}}dx$ evaluate to? This is expectation of ...
0
votes
1answer
31 views

Standard normal distribution inequality

I want to know how to prove the following inequality that seems to be true numerically. Let $n(x)$ be the density of the standard normal, and $N(x)$ be the cdf of standard normal. Then, for $x\geq ...
0
votes
0answers
21 views

Converting one normal distribution to another

I have a long data similar to this; between 15 and 25 consider its mean as m and calculated standard deviation using this formula. I assumed the above data as a normally distributed data and can ...
0
votes
0answers
21 views

Normal Distribution and optimization

Suppose the radius $X$ (in mm) of certain kind of water pipes follows the normal distribution $N(\mu,1)$. If the radius is less than 10 or larger than 12, then it is failed product. Suppose the ...
1
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1answer
17 views

Normal approximation to Binomial probability distribution

Where did this 0.5 come from? I understand we are using Z-score but in my calculations I basically omit the 0.5 to get a probability of .9616.
0
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2answers
51 views

Equation with normal distribution function

I was working on a task in probability, and got stuck at this: $ϕ(\frac{x-50}{4}) - ϕ(\frac{-x-50}{4}) = 0.6$ ($ϕ$ is the normal distribution function.) It's so simple, yet I don't know what to do ...
0
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1answer
35 views

normal distribution strange probability

Given the particular normal distribution specified below, what is the probability that a random observation falls within the specified range .004 greater and less than the average? original Lower ...
0
votes
1answer
25 views

How to calculate covariance of X and Y given joint probability

$X$ and $Y$ are dependent variables both normally distributed as $N(\mu-const, \sigma^2)$. I don't know what the joint distribution is. I know that when $const = 0$, then the joint probability ...
1
vote
3answers
50 views

Normal distribution exercise!

If a technician does not encounters any hardware problems, the time he requires to assemble a computer follows a normal distribution with a mean of $30$ minutes and a standard deviation of $3$ ...
0
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0answers
14 views

Normal distribution problem using R

The elongation of a steel bar under a particular load has been established to be normally distributed with a mean of $\mu = 0.05$ and a standard deviation of $ \sigma = 0.01$. Find the probability ...