0
votes
0answers
11 views

Combining independent Gaussian probabilities

I am using three Gaussian distributions with which I generate random numbers to represent many candidate xyz points. I use some selection criteria (details not particularly relevant) to decide on ...
2
votes
1answer
23 views

Marginalization of a paramter in Gaussian

If $\theta \sim N(\mu,\sigma_o^2)$ and $\mu \sim N(0, \sigma_1^2)$ what is the marginalized $P(\theta)$. Is it $N(0,\sigma_o^2+\sigma_1^2)$?
1
vote
1answer
21 views

Normal Distribution and Probability on Excel

The size of fish in a lake follows a Normal Distribution with mean m = 1 lb 4 oz and standard deviation s = 3 oz . Fish that weigh less than 1 lb 9 oz must be released back into the lake. Bill ...
1
vote
1answer
22 views

Expected value of normal distributed variable

I need to calculate the expected value of a modified normal distributed variable but i'm struggling. So maybe someone can help me. Suppose we've got a normal distributed variable $X \sim ...
4
votes
1answer
137 views

Why does this determinant have a continuous density at zero?

This question is a simplification of my previous question. I think this is easy, but I don't have a strong enough background in probability. Let $A$ be a random $n\times n$ real matrix that satisfies ...
0
votes
0answers
21 views

GEV of Normal Distribution and relationship of the parameters

My question goes on Extreme Value Theory for the Normal distribution: 1) Which GEV (Generalized Extreme Value distribution) type is the Normal distribution(Weibull/Gumbel/Frechet)? 2) If we have the ...
0
votes
1answer
26 views

How to add standard deviation regarding MATLAB function normrnd(mu,sigma)?

My question depend on this scenario which is as follows, I used a MATLAB function "normrnd(mu,sigma)" with mean 'mu = 0' and S.D 'sigma = 5', to generate a normal random number "R1". I added this ...
0
votes
1answer
36 views

Approximation in Normal distribution random variable

Let ${X_n : n \geq 1}$ be independent $\mathcal{N}(0,1)$ random variables. How do we get the following approximation?
0
votes
1answer
40 views

Find the probability that the average of X and Z is greater than Y. Where X, Z, and Y are normal RVs.

Here is the exact statement: Suppose X,Y , and Z are independent random variables. X is a normal random variable with mean 5 and variance 16, Y is a normal random variable with mean 7 and variance ...
1
vote
2answers
47 views

Concept of Probability in math first level

I am trying to teach myself the concepts of probability and I was wondering if this is correct. I am only 13 years old and did not learn this yet. I am just reading parts of a probability book to get ...
-2
votes
1answer
54 views

I would like some help please in utilising the normal distribution.

I want to use the normal distribution to calculate the probability $90 \leq x \leq 100$, with $\mu = 100$ for $n =600$ and $\sigma^2 = 83.333$. Now I think this means $\frac{90 - 100}{\sqrt{83.333}} ...
0
votes
0answers
29 views

What distribution to use?

I am just discussing this with my professor as part of a project. So people sign a contract with us to become a membership. And we hold events for them to come(think about this as some club you need ...
1
vote
2answers
82 views

Sum of two truncated gaussian

What is the CDF and the PDF (or approximation) of the sum of two truncated gaussian $X = TN_x(\mu_x,\sigma_x;a_x,b_x)$ and $Y = TN_y(\mu_y,\sigma_y;a_y,b_y)$ ? where $TN(\mu,\sigma;a,b)$ is a ...
2
votes
1answer
23 views

Normal Distribution burnout… of lightbulbs.

Thank you for looking through this problem, much appreciated! I tried to work out the answer for a, but I got .2946 when the actual answer is .3085... How do I start this? By the way, I just want to ...
1
vote
2answers
33 views

The Normal Distribution in measuring two towers…

I understand the explanation and the math behind the problem, all I am asking for is a quick explanation behind this. "Two instruments are used to measure the height, h, of a tower. The error made by ...
0
votes
1answer
7 views

Bivariate Normal Probability

Assume we have a large data set of PSAT and SAT scores with bivariate normal distribution with $\rho = 0.6$. The mean and SD of the PSAT scores are (respectively) $1200$ and $100$. The mean and SD ...
0
votes
1answer
16 views

$\mathbb{P}(|X|<1,|Y|<2)$ When $X,Y$ Are I.I.D. Standard Normal

Calculate $\mathbb{P}(|X|<1,|Y|<2)$ when $X,Y$ are i.i.d. standard normal r.v.s. I think the answer is simply $$(\Phi(1)-\Phi(-1))(\Phi(2)-\Phi(-2)).$$ Is this correct? Thanks.
0
votes
1answer
22 views

An IB Math HL question on normally distributed random variable.

Some Background: Tim goes to a popular restaurant that does not take any reservations for tables. It has been determined that the waiting times for a table are normally distributed with a mean of ...
0
votes
1answer
24 views

Moment Generating Function of Gaussian Distribution

Derive from first principles, the moment generating function of a Gaussian Distribution with $$PDF= \dfrac{1}{\sqrt{2\pi \sigma^2}}e^{-(x- \mu)^2/2\sigma^2}$$ MY ATTEMPT MGF= E[$e^{tx}$]= ...
0
votes
2answers
75 views

Distribution of mean of Normal distribution

Suppose $X\sim N(\mu,\sigma)$. I want to find the following probability $P[\mu \ge \theta |x= \theta -c]$ for $c>0$. In another word, I saw a sample of Normal distribution, $x$, and know that it ...
0
votes
0answers
28 views

How to compute the expected value of normal distribution over a finite interval.

The occurrence time of event A is normally distributed with mean $\mu=200$ and variance $\sigma^2=10^2$. That is, $f(A) \sim \mathcal{N}(200, 10^2)$. As known, the expected occurrence time of A can ...
0
votes
0answers
45 views

Expectation of normal CDF with truncation

Suppose that $a$ and $T$ are given positive numbers. I would like to evaluate $$\begin{align*} \mathbb{E}\left[\Phi\left(aX\right)\mu\left(X+T\right) \right],\tag{1} \end{align*}$$ where ...
1
vote
1answer
29 views

Normal distribution without standard deviation given

The proportion of pink candies in a bag is supposed to be $50\%$. The filling machine is to be tested to see if it fills with the right proportion. A random sample of $50$ candies is made. The machine ...
1
vote
2answers
39 views

When do normal distributions not occur?

I know that in many cases one can assume a normal distributed probability density. But what the situations when the distribution in non-normal. Some examples would be nice. For example, suppose ...
0
votes
0answers
18 views

Estimation for expected value of a combination of two normal distributed random variables

I am struggeling to understand the proof of the following Lemma. Let $\epsilon_1$, $\epsilon_2$ be $\mathcal{N}(0,1)$ random variables. Then $\forall$ b $\geq$ 0 and $\forall$ c $\geq$ 1 there is an ...
3
votes
0answers
51 views

Independent normal distributions

I found two theorems with a similar content and want to find out which one is true: Let $X,Y$ be normally distributed random variables and $X+Y$ is also normally distributed or $ (X,Y)$ is ...
1
vote
1answer
35 views

moment generating function of normal distribution

I know this question relates to the chi-squared distribution, but I think what the question wants me to do is somehow derive this distribution from the information given. I have a normally ...
1
vote
2answers
45 views

Bivariate normal distribution question

If I have $(X,Y)$ with joint density $f(x,y)$ and $A$ is an invertible $2\times 2$ matrix, then for the random vector $(W,V)$ defined by: $$ \begin{pmatrix} W\\ V \\ ...
2
votes
1answer
46 views

Calculation of distribution of a gaussian process

Currently finishing the last year of PhD in statistics, we wonder if you could help us with the following. Let $T = [0,1]$ and $X = \left( X_{t}, t \in T \right)$ be a gaussian process with mean ...
-1
votes
1answer
51 views

What's the pdf of $Z=X^2 +2X$ if $X$ is a standard normal? [closed]

Le be $X$ distributed as a standard normal. What is the density function of $Z=X^2 +2X$? Thanks for your help
0
votes
1answer
25 views

P-P plot and Q-Q plot

How to draw P-P plot and Q-Q plot manually ? I have looked at different site and they explained in various way, such as one said for p-p plot in X-axis there is residual in ascending order and in ...
1
vote
1answer
21 views

limiting behavior of standard normal survivor function [duplicate]

How do you show that $\lim_{x\to \infty} 1-\Phi(x) \sim \phi(x)/x$? In the previous, I'm using $\Phi$ to refer to the standard normal CDF and $\phi$ to refer to the standard normal pdf. Thanks!!
0
votes
2answers
35 views

Binomial and Normal Distribution Problem - Check solution

Whooping cough is a highly contagious bacterial infection...About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% of vaccinated ...
1
vote
1answer
14 views

Normal Distribution how $N(x-x_n|0,\sigma^2) = N(x |x_n,\sigma^2) $

I read an expression Could someone explain the step $N(t-t_n|0,\sigma^2) = N(t | t_n,\sigma^2) $ ?
1
vote
0answers
16 views

What is the minimum standard deviation for a normal PDF such that one tail is always larger than that of a second normal PDF (different means)?

Say I have two weighted normal distributions, $$ f_1(x) = \frac{a}{2 \sigma_1} e^{-\frac{(x-\mu_1)^2}{2\sigma_1^2}} $$ and $$ f_2(x) = \frac{1-a}{2 \sigma_2} e^{-\frac{(x-\mu_2)^2}{2\sigma_2^2}} $$ ...
0
votes
1answer
23 views

Distribution of distance from 0 of gaussian point

Suppose $X_1,...,X_d\sim\mathcal{N}(0,1)$ are i.i.d.'s, each distributed normally around 0 with variation 1. It looks like $\mathbb{E}\left(\sum X_i^2\right)=d$. Why is that true? And how $Y=\sum ...
1
vote
1answer
137 views

mean and variance normalization of vectors

I have vectors $x \in \mathbb{R}^n$ and I expect some multivariate normal distribution. I want to normalize the vectors in such a way that $y = M (x - b)$ has mean zero ($\operatorname{E}[Y] = 0$) ...
0
votes
1answer
36 views

Standard deviation with multiple means and deviations

The amounts of a certain mineral that can be produced in a day from mines $1$, $2$, and $3$ are independent normal random variables with means equal to $80$, $90$, and $75$ pounds, respectively, ...
1
vote
1answer
22 views

Exponential deviation with two $x$ values

I recently got interested in this topic of standard deviation. My TA did not have any time to go over this topic so I was trying to teach myself it recently. My TA said if he had more time he would ...
2
votes
1answer
68 views

Central Limit Theorem for uncorrelated (non-independent) but bounded random variables

Given uncorrelated, discrete random variables $X_i$ that are bounded, e.g., they can only take on values $|X_i| \leq 4$, then is there a form of the central limit theorem that one can apply to the ...
2
votes
1answer
38 views

How to find $E[X|X>Y]$

Suppose $X$ and $Y$ are independent standard normal variable. I want to find $E[X|X>Y]$. I calculated that $$ f_{X>Y}(x) = 2\Phi(x)\phi(x)$$ However I couldn't find the expected value using ...
0
votes
1answer
20 views

Standard normal RV probability

Z is a standard normal random variable I need to find $P(|Z|<.95)$, find c such that $P(|Z|<c)$, and given that X is a RV with mean 3 and standard deviation 16, find $P(X>3.84)$ I am just ...
0
votes
0answers
13 views

Gaussian measure of a convex hull with respect to scaling.

consider the following problem: Let $m\geq 1$ and consider $a_1,\ldots,a_{m+1}\in \mathbb{R}^m$. Let $A=(a_1,\ldots,a_{m+1})$ be the matrix having the $a_i$ as columns. Let ...
0
votes
0answers
17 views

Solving for the mean given the probability and standard deviation

X is a continuous random variable where $X$ ~ $N(u, 2^2)$. Find $P(-0.524 < X - u < 0.524)$. I thought that the probability for this would be .68 because it is separated by two standard ...
1
vote
1answer
30 views

Is normalcdf() inclusive?

I was looking at these examples here: Example 1: Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5. Find: a) the probability that a value is ...
0
votes
0answers
17 views

Distribution curve problem

The distribution curve shown corresponds to ${X}$~N${(μ, o^2)}$. Area A = Area B = 0.2. Find μ and ${o}$. I tried using the z-score forumla with: ${-.2o + μ = 20}$ and ${.2o + μ = 38}$ and ...
1
vote
0answers
17 views

Continuity Correction with replacement

An urn contains 2 white and 8 red marbles. A marble is drawn from the urn 100 times in succession with replacement. What is the probability of drawing more than 75 red marbles? My attempt: $n=100, ...
0
votes
0answers
24 views

Normal Distribution while finding sigma

I was reading some things about normal distribution and saw this problem in a text a couple days ago. I know it might be a little advanced for me at the moment, but I was wanted to know if someone can ...
0
votes
1answer
36 views

If speeds of two cars are Normal RV s, what is the distribution of the distance between them?

The speeds of two cars are random variables that follow $N(\mu_1,\sigma_1)$ and $N(\mu_2,\sigma_2)$ distributions.They start simultaneously. Let X be the distance between them after m hours. (Note ...
1
vote
1answer
41 views

Showing the normal distribution has points of inflections at $x = \mu \pm \sigma$ and a maximum at $x = \mu$

$X \sim N(\mu, \sigma^2)$ I.e. the density of $X$ is the normal distribution. I am looking to show that $f_X(x)$ has points of inflections at $x = \mu \pm \sigma$. In my notes it says that we ...