Tagged Questions
1
vote
2answers
92 views
Function with variable having gaussian distribution
If I have a variable $X$ whose Gaussian distribution is known and let $f$ be a known function, is there a way to compute $f(X)$ i.e. the resulting Gaussian distribution from this? Is the result ...
2
votes
1answer
90 views
Asymptotic probability concerning the largest absolute value in an iid Gaussian sample
Let $v[n]$ be a vector $N$ $iid$ gaussian samples, of ~$N(0,\sigma^2)$ Also, let $v_{max}$ denote the maximum absolute value of all the samples given. (That is, if I took the absolute value of all the ...
0
votes
0answers
25 views
Probability that a given Normal Distribution is Maximum among others [duplicate]
You are given the mean and standard deviations of N normal distributions x1,x2...xn
What is the probability that x1 is maximum?
ie. Find P(x1>x2,x3..xn)
How do I go about solving this?
x1,x2,x3 etc ...
0
votes
0answers
42 views
Determining sample size in a non-normaly distributed data
I want to take some samples from a database nearly ~150.000 records of a non-normally distributed values. From this link I obtained some common procedures to find a sample, influenced by The level of ...
0
votes
0answers
51 views
How to compute probabilities of normally distributed variables?
Let $X_1, X_2, \ldots, X_{16}$ be independent with $N(3,4)$ distributions and $\bar{X}$ denote the sample mean. Find:
$P(-8 < 2 \bar{X} < -4)$.
A number $K$ such that $P(-K < 2 \bar{X} ...
2
votes
0answers
40 views
Order statistics of equal correlated continuous random variables
Suppose that $X_1, \ldots, X_n$ are mutlivariate normal with equal correlation
$\rho$ and each of them are marginally
distributed as $N(0,1)$. Let $X_{(1)}, \ldots, X_{(n)}$
be the corresponding order ...
0
votes
2answers
70 views
Normal approximation to binomial
What do I do when the normal approximation is not valid?
Here's the question I'm trying to answer:
A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
0
votes
0answers
49 views
Normal Distribution [duplicate]
Using the normal distribution. Let $X\sim \mathcal{N}(1, 2)$ and $Y\sim \mathcal{N}(2, 3)$ where $\mathcal{N}(μ, \sigma^2$)
denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. X ...
0
votes
1answer
237 views
Finding the z score and p-value of a binomial distribution
Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
0
votes
2answers
109 views
Why doesn't this represent a normal approximation to the binomial?
Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
2
votes
1answer
332 views
probability of one random variable being greater than another
Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.
...
2
votes
2answers
70 views
8
votes
1answer
291 views
Central limit theorem and the law of large numbers
I have a very beginner's question regarding the Central Limit Theorem (CLT):
I am aware that the CLT states that a mean of i.i.d. random variables is approximately normal distributed (for $n \to ...
-1
votes
1answer
198 views
Combined probability of multiple Gaussian experiments with differing observations [closed]
Observations of three independent Gaussian experiments have yielded probabilities of .1, .2 and .9. I'm trying to accept or reject a hypothesis that the results can be explained by Gaussian behavior. ...
1
vote
1answer
79 views
Flying Bomber aircraft through SAM sites - combining normal distributions
I have been puzzling over this for days but I don't think this was covered at school
We simultaneously fly a known number of bomber aircraft, K, through three sequential batteries of surface to air ...
0
votes
0answers
44 views
Comparing two different leagues of similar but not equal distributions around a standard deviation of error of a prediction from a rating system
This query ties a lot of my interests in rating sports teams together, because as I’ve mentioned before I do a version of the Kenneth Massey method (as per his 1997 thesis ...
0
votes
1answer
94 views
How to find the joint density of 3 normal variables?
Suppose $U, W, V, S$ are four independent normal random variables with mean $0$ and variance $1$. Let $X=W+U$, $Y=2W+S$, $Z=3W+V$. What is $f(X, Y, Z)$?
Thanks!
15
votes
3answers
384 views
Confidence Interval for variance given one observation
This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory":
Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters ...
3
votes
2answers
180 views
What is $P(X_1>X_2 , X_1>X_3,… , X_1>X_n)$?
All $X$ are mutually independent and from normal distributions, each with its own mean and variance. If it's easier, $P(X_1 \geq X_i \forall i \in \{1, ..., n\})$ is fine although I suspect it's the ...
2
votes
1answer
122 views
Product of Independent Gaussian Variables
Let $X$ and $Y$ be two independent normal distributions according to $X\sim\mathcal{N}(0,P)$ and $Y\sim\mathcal{N}(0,Q)$. Is it true to say the following ?
...
4
votes
0answers
50 views
How to pick from a set of random variables the one with the highest mean using a fixed number measurements?
Suppose we have $N$ approximately normally distributed continuous random variables $X_1, X_2, X_3, \ldots,X_N$, each with an unknown mean and variance. I'd like to find the random variable with the ...
6
votes
2answers
205 views
Which is largest, of a bunch of normally distributed random variables?
I have random variables $X_0,X_1,\dots,X_n$. $X_0$ has a normal distribution with mean $\mu>0$ and variance $1$. The $X_1,\dots,X_n$ rvs are normally distributed with mean $0$ and variance $1$. ...
5
votes
3answers
315 views
Probability of collision (two bivariate normal distributions)
I am trying to solve this problem on and off for the past couple of months but to no success. This was supposed to be a very small part of my PhD thesis in navigation but I guess I underestimated the ...
2
votes
1answer
149 views
Probability error - binary message
Please, I need some support (not solution) and input to know if the way is right to go on.
Consider the communication of binary messages in a transmission medium. Any message sent is selected from ...
0
votes
1answer
164 views
Joint probability and Gaussian copula
I have $\Pr(A)=29\%$ and $\Pr(B)=10\%$, where $A$ and $B$ are two events which are not independent.
In fact, a correlation measure suggests they're correlated by $\rho=0.8$.
I would like to ...
4
votes
1answer
163 views
Inequality for bivariate normal distribution
Let $X_1$ and $X_2$ be bivariate normal with mean $\mu=(0,\mu_2)$, for any $\mu_2$, and correlation $\rho$.
Consider the following inequality:
\begin{align*}
Pr\left\{|X_1| \ge ...
2
votes
3answers
471 views
Normal approximation to the binomial distribution
I am having trouble getting to the bottom of this concept for two types of questions (hw is already passed, but I have a test this week and would like to do better). Hopefully someone can help me get ...
1
vote
3answers
262 views
Given a normal distribution, a mean, and standard deviation what is the probability a Variable is in a range [duplicate]
Possible Duplicate:
Normal distribution probability
Issues getting to the bottom of a HW problem, but I am not looking for the answer, just some guidance.
x has a normal distribution with
...
3
votes
1answer
174 views
Order statistics of absolute value of bivariate normal distribution
Suppose $X_1$ and $X_2$ are bivariate normal and let $|X|_{(1)}$ and $|X|_{(2)}$
be the ordered version of their absolute value. I am interesting in finding the following probabilities or some bounds ...
1
vote
0answers
88 views
How do I calculate the Bayes error of a multivariate normal Bayesian classifier?
I have a 4 dimensional feature and each of them are independent normal distributions. I want to calculate the bayesian error associated with this classifier. The covariance matrix and the mean have ...
3
votes
1answer
181 views
Is a vector of normal random variables ever -not- multivariate normal [duplicate]
Possible Duplicate:
Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?
In the Wikipedia entry on the multivariate normal ...
0
votes
2answers
101 views
Cental limit theorem for average of iid variables
The Wikipedia entry on the CLT states at one point: "For fixed large $n$ one can also say that the distribution of $S_n$ is close to the normal distribution with mean $\mu$ and variance ...
4
votes
1answer
94 views
What is the maximum value in a finite selection of a normally distributed variable?
A parameter of an object is normally distributed with a mean m and a std. dev. s. If r such ...
0
votes
1answer
40 views
Probability of an event occuring [duplicate]
Possible Duplicate:
How to find percentiles of a Normal distribution?
The weight of a given Africander breed is said to follow a normal distribution with mean 200 kg and standard deviation ...
7
votes
1answer
185 views
“Since $x$ is near-gaussian, its PDF can be written as…”
Short question: Why is this true??
Long question:
Very simply, I am trying to figure out what justifies this first equation. The author of the book I am reading, (context here if you want it, but ...
1
vote
1answer
96 views
Finding ways to bid for items, which has a normal distributed price
This is an interview questions, I am not quite sure how to solve. The question is stated as this:
Suppose that you want to buy a specific type of car, but you don't know anything about cars (you ...
2
votes
0answers
99 views
Continued fraction representation of the multivariate normal distribution [closed]
Can anybody help me with a continued fraction representation of the multivariate normal distribution? Such a representation is well-known for the univariate case; see, for example,
C-I. C. Lee. On ...
1
vote
2answers
117 views
Significance of different mean values for two processes
I have an experiment that produces one measurement every time it is run. I can change something in the experimental setup, and I want to test if this change in the setup results in a change of the ...
0
votes
0answers
42 views
How to compute CDF probability of normal distribution [duplicate]
Possible Duplicate:
Evaluate definite interval of normal distribution
Title was changed and question edited bellow.
How is possible that a probability density function defined as following ...
0
votes
1answer
100 views
How can I replace this condition by a probability?
I want to see if a datapoint x should (or not) be assigned to a nearest component y using the following condition:
if ($d > T$) then {do not assign x to y}. With $d = distance(x,y)$ and $T = ...
1
vote
1answer
113 views
How to equate hit probabilties on 2 different surfaces
I'm looking for help in determining how to equate the following:
We have a surface of 13 cm X 10 cm.
We have a 95% probability of hit
on a 16 cm diameter surface.
I would like to equate $B$, ...
-1
votes
1answer
95 views
What is probability to get through to the value
I have data set of ints with values 1..10.
Before any sample is added to the dataset it can be observed for a period of time. During this period X can grow from 1 to 10 (Note : it only grows in one ...
0
votes
1answer
57 views
Conditional on Gaussian, need clarification
I'm reading Andrew Ng's notes on machine learning, and on page 12 of this document, he makes a step in his proof that I'm trying to decipher:
Let $\textbf{x} = \left( 1 , x_1 , x_2 , \cdots , x_n ...
2
votes
1answer
498 views
Convergence in probability and $L_2$ for normal random variables
In an answer here: Convergence of identically distributed normal random variables, the following lemma is mentioned:
Lemma: Let $X_1, X_2, \ldots$ be a sequence of zero-mean normal random
...
6
votes
1answer
357 views
How can I prove the experiment data follows heavy-tail distribution?
I have several test results of server response delay. According to our theory analysis, the delay distribution (The probability distribution function of response delay) should have heavy-tail ...
1
vote
1answer
366 views
Perfectly correlated (normal) random variables
I am not sure in the terminology, so I will simply try to explain the situation that I would like to model as I see it. Suppose there is a set of random variables. The variables are correlated in such ...
2
votes
2answers
1k views
Linear combination of two dependent multivariate normal random variables
Suppose we have two vectors of random variables, both are normal, i.e., $X \sim N(\mu_X, \Sigma_X)$ and $Y \sim N(\mu_Y, \Sigma_Y)$. We are interested in the distribution of their linear combination ...
5
votes
3answers
445 views
Probability of winning a tournament
Edited Question:
As I promised I've edited this question. The previous version was written with the intention of simplifying the real question, but it ended in losing the real significance. Now I'm ...
4
votes
2answers
468 views
Is the variance of the multivariate folded normal distribution known?
The mean and variance of the folded normal distribution are known. Consider now the distribution of $(|x_1|, \ldots, |x_n|)$, where $\mathbb{x} \sim N(\mu, \Sigma)$. The mean of the multivariate ...
3
votes
1answer
146 views
What is the probability that two independent random vectors with a given euclidean distance $r$ fall in the same orthant?
Consider two independent and identically distributed random vectors of dimensionality $N$, $\mathbf{x}$ and $\mathbf{y}$, where their elements are iid generated from a Gaussian with zero mean and ...
