Tagged Questions
0
votes
1answer
35 views
How do I prove Poisson appraches Normal distribution
I want to prove why the mean and variance of a $\operatorname{Poisson}(\lambda)$, is different when the time index approaches infinite (it's approximated by the mean and variance of a Normal).
For ...
0
votes
0answers
25 views
Convolution of logistic function and gaussian distribution
I am trying to solve the folowing problem:
$$\int \exp\left(-\frac{(x-u)^2}{2\sigma^2}\right) \log(1+\exp(ax + b)) \,dx$$
which I think is very complicated and there is no closed form solution(?)
...
0
votes
0answers
21 views
Multivariate Normal Product Distribution
I am looking for multivariate case of a distribution of a product of two normally distributed variables X and Y. The variables are independent. Something similar to this:
...
5
votes
1answer
105 views
How was the normal distribution derived?
Abraham de Moivre, when he came up with this formula, had to assure that the points of inflection were exactly one standard deviation away from the center, and so that it was bell-shaped, as well as ...
0
votes
0answers
17 views
how to obtain the moments of skew-normal distribution?
the moment generating function of a skew normal distribution of random variable, z is defined as,
$$
M(t) = 2(e^{(t^2/2)})\Phi({{\delta}t)}
$$
where,
$\Phi$ refers to cumulative distribution function ...
0
votes
2answers
45 views
Calculating the MSE for assessment
Let $X_1, \ldots, X_n \sim \mathcal{N}(\mu, \sigma^2)$ be the sample, when $\mu$, $\sigma$ are unknown.
We suggest assessment for $\sigma^2$:
$$S^2 = \frac{\displaystyle\sum_{i=1}^n (X_i - ...
0
votes
0answers
30 views
Homework Help. Probability Density Functions.
$X$ is $N(10,1)$. Find $f(x|(x-10)^2 < 4)$
This is a homework question. I can only figure out that X is normally distributed with mean 10 and variance 1.
Can you please explain what is meant to ...
0
votes
0answers
41 views
How to normalize a set of vectors
I have a set of vectors $\displaystyle a_1, a_2,...,a_n$ and each of which has a dimension of $k$. How can I normalize the elements of these vectors to make them lie within $[0,1]$?
I was thinking ...
1
vote
1answer
56 views
Derive the PDF of the log-normal distribution?
If $X \sim N(0,1)$ and $Y = e^X$, find the PDF of $Y$ using the two methods:
(i) Find the CDF of of $Y$ and then differentiate. Use the notation $\Phi(x)$ and $\phi(x)$ for the CDF and PDF of $X$ ...
1
vote
3answers
47 views
Standardizing A Random Variable That is Normally Distributed
To standardize a random variable that is normally distributed, it makes absolute sense to subtract the expected value $\mu$ , from each value that the random variable can assume--it shifts all of the ...
0
votes
0answers
34 views
Can Bhattacharyya distance be greater than one?
I have two vectors, say $P$ and $Q$. I want to find the statistical overlap between two given that $P$ is my reference which I have modeled after Normal distribution and I have parameters for it. $Q$ ...
-1
votes
1answer
17 views
Bound for normal distribution
suppose $X$ is a standard normal distribution then what is the bound for
$Pr \{|X|\leq \epsilon \} $, where $\epsilon \geq 0.$
0
votes
1answer
28 views
Normal distribution help please
Under what conditions can the distribution of the mean be approximated by a normal distribution if the distribution were not normal.
1
vote
0answers
132 views
Hypothesis testing of normal distribution, known mean unknown variance
I've been working on review problems, and this one has me completely stumped.
Let $X_1 ... X_{10}$ be a random sample from a $N(3,\sigma^2)$ distribution, where $\sigma^2$ is unknown. Using the ...
0
votes
0answers
17 views
How to test whether there is an association between two data fields by testing a hypothesis?
The table below cross classifies Education by Employment Confidence and is
based on a sample 1363 randomly selected adult respondents in China.
Highest degree Employment Confidence Total
...
0
votes
0answers
31 views
Using an appropriate hypothesis to test whether two means are different
Manager examined potential differences between two models of bicycles. The
mean life of the bicycles is of primary concern. The followings table provides the
available date which measured in ...
-1
votes
3answers
72 views
Variance of transformed random variable
The relationship of two random variables is given by
$$ X = \Phi(Y) \Leftrightarrow Y = \Phi^{-1}(X),$$
where $\Phi(\bullet)$ is the standard normal cdf and $\Phi^{-1}(\bullet)$ the inverse of the ...
1
vote
0answers
82 views
Bayesian posterior with integrals over normal densities
Realizations from normal distributions with known precision are used to estimate the mean, but the realizations are not always precisely observed. Instead, only a range of the realization is observed. ...
1
vote
3answers
89 views
Let $ X_1,X_2,…,X_n$ be i.i.d. $N(\theta_1, \theta_2)$, please prove that $E[(X_1-\theta_1)^4] = 3\theta_2^2$
If $X_{1}$, $X_{2}$, ..., $X_{n}$ is sampled from $N(\theta_1, \theta_2)$, how can I prove that $E [(X_{1} - \theta_1)^{4}] = 3 \theta_2^{2}$?
I started off this question finding the completely ...
0
votes
0answers
48 views
Inverse of a random variable when distributed normally
If $$x_{t}=\rho\cdot x_{t-1}+e_{t},$$ where $e_{t}\sim N(0,\sigma)$. What is $E(1/x_t)$?
0
votes
0answers
20 views
Interval Estimation when $\overline{Y}$ and $S$ is unknown.
Question: A random sample of size $n=9$ is drawn from a normal distribution with $\mu=27.6$. Within what interval $(-a,+a)$ can we expect to find $\frac{\overline{Y}-27.6}{S/\sqrt{9}}$ $80$% of the ...
1
vote
1answer
56 views
Chance of two Gaussian distributions being observations of the same phenomenom?
For an algorithm used for generation of a road map based upon position-samples, I am looking for a method of determining the probability of a sample belonging to an already discovered element of the ...
0
votes
0answers
31 views
What are NSCORES?
I was reading a page I found on the web about the Normal Distribution.
They give an example with some data here:
...
2
votes
1answer
54 views
Log-likelihood for multinominal normal distribution
Given $n$ jointly-normal random variables $X_1, X_2, \dots, X_n$, with
$$\mu_i=\mu\forall i \in\mathbb{N}^+$$
$$\sigma_i=\sigma\forall i$$
$$\rho_{i,j}=\rho\forall i,j \mbox{ with } i\neq j$$
what is ...
0
votes
1answer
60 views
Histogram with Gaussian bell curve
How do I create/calculate the probability density curve in a histogram which is scaled to the frequency axis with ABSOLUTE values (example)? The curve should be based on the calculated average and the ...
2
votes
0answers
109 views
Standardized Normal Distribution Problem
Mopeds (small motorcycles with an engine capacity below $50~cm^3$) are very popular in Europe because of their mobility, ease of operation, and low cost. The article “Procedure to Verify the ...
1
vote
1answer
60 views
Determining The Value, c, A Random Variable Assumes
The question I am working on is:
In each case, determine the value of the constant c that makes the probability statement correct.
$P(c \le |Z|)=0.016$
Here is my attempt:
$P(|Z| \ge ...
2
votes
0answers
102 views
Simplifying covariance matrices in distributions
In the multivariate Gaussian distribution, it is required that the covariance matrix be positive semidefinite. I have read that a positive semidefinite matrix $\Sigma$ can be written as $LL^{T}$. I ...
1
vote
1answer
83 views
statistics: probability, normal distribution
The time that customers take to complete their transaction at a money machine is a
random variable with mean $\mu$ = $2$ minutes and standard deviation $\sigma$ = $0.6$ minutes.
About 30% of ...
2
votes
1answer
57 views
Expected value of $xx^{T}$ for multidimensional Gaussian
I need a bit of help understanding a step in the derivation of the expected value of $\bf{x x^{T}}$, that is, $E[\bf{x x^{T}}]$ with a Gaussian distribution.
By definition, using the D-dimensional ...
0
votes
0answers
81 views
Standard deviation of the weighted mean
How do you find the standard deviation of the weighted mean?
The weighted mean is defined: $\bar{x} = \frac{\sum{wx}}{\sum{w}}$
The weighted standard deviation (since it is not specified, I take it ...
1
vote
1answer
104 views
Find a Probability of a Normally Distributed Random Sample
Please help me figure out how to do this problem. I need to be able to understand how to solve problems like this.
Thanks times a million!
Problem: An employer is interested in the commute times for ...
0
votes
0answers
40 views
Calculating Probability a Population is Normal Given a Sample
A lecturer is delivering a speech to 1000 people. She is meeting people in the audience and testing the hypothesis that the audience has a normal distribution of third sons (assuming that 200/1000 is ...
1
vote
1answer
92 views
Rayleigh distribution
I have this question from my statistical theory course:
A sniper shoots at a target. X and Y measure its deviation on the x and y axes. X and Y are independent and are distibuted normally with mean=0 ...
1
vote
1answer
40 views
What is the physical meaning of the output/ y -value of a normal distribution? (not the area under its curve)
Forgive me for my lack of knowledge regarding math terminology.
I'm learning basic statistics right now, and I can see pretty intuitively that the area under a normal distribution on a certain ...
0
votes
1answer
66 views
Gaussian random variable(GRV)
$X$ is a Gaussian random variable $N(2,2)$. Also given are values x1=1 and $x=3.
i. Write a program to calculate the probability Pr(x1 ≤ X ≤ x2).
ii. Write a program to calculate the probability Pr(|X ...
0
votes
0answers
31 views
Standard deviation of a particular dimension in a multivariate Gaussian distribution
I have a set (cluster) of vectors in dimension $d$. From this I have calculated the sample mean and covariance matrix ( I make the assumption that they are from a multivariate Gaussian).
My question ...
2
votes
2answers
84 views
What is the probability that two samples represent the same normal distribution?
Yes, it's a basic question. But, I have searched about 25 web pages for this and found only things that were irrelevant or incomprehensible. So I have indeed tried.
My question is: I have two ...
-2
votes
1answer
58 views
Normal Distribution Stats
Let $$ X \sim N(65,20) $$
Find correct to $3$ Decimal Place the value of $x$ such that $Pr(X>x) = 0.43$
0
votes
1answer
72 views
Percentage point of Normal Distribution.
Let $$X \sim N(65,64) $$ Find the lower $2$% point for $X$; that is, find the value of $x$ such that $Pr(X<x) = 0.02 $
i know i need to do something like $\frac{X- 65 }8 = ... $ but not ...
0
votes
0answers
83 views
Statistics Question - Normal Distribution
The scores of a final exam have a Normal Distribution with mean $75$ and standard deviation 6. An independent sample size of $9$ is drawn from this distribution. The corresponding random variables are ...
0
votes
1answer
83 views
How can I solve this integral?
How can I solve the following integral?
$$\int_{-\infty}^\infty \prod_{i=1}^n \bigg( 1 - \Phi\left(\frac{c - \mu_i}{\sigma_i}\right) \bigg) \frac{1}{\sigma_Y}\phi \bigg(\frac{c-\mu_Y}{\sigma_Y} ...
0
votes
1answer
98 views
How to count $n$th percentile from normally distributed random variable?
I have normally distributed random variable $X\sim \mathcal N(100,225)$. How to count $n$th percentile?
In my case I need lower quartile - $x(0.25)$.
3
votes
1answer
280 views
How to check if my dataset is normally distributed?
I have data sets (measurements) and I need to know if values are normally distributed. I would like to get this information programmatically in my application and not via plotting and checking it ...
0
votes
1answer
51 views
How to estimate parameters of a normal distribution?
Suppose one knew that 105 workers were evaluated by their boss. Such evaluation is distributed according to a normal distribution with mean $\mu$ and std. deviation $\sigma$. We also know that 20 ...
1
vote
1answer
57 views
Normal Distribution Identity
I have the following problem. I am reading the paper which uses this identity for a proof, but I can't see why or how to prove its true. Can you help me?
\begin{align}
\int_{x_{0}}^{\infty} e^{tx} ...
0
votes
3answers
112 views
Integrating the pdf of a normal distribution
I need to find the distribution of $Y=X_1+X_2$ where both $X_1$ and $X_2$ are normally distributed with $(\mu,\sigma^2)$.
So I'm looking for ...
0
votes
1answer
65 views
moment generating functions by integration
Let X~N(0,1)m find the moment generating function of $X^2$ using integration techniques.
I'm not sure exactly what this is asking me to do. Is $X^2$ just the pdf for the standard normal function ...
0
votes
0answers
52 views
What does taking the logarithm of a variable mean?
Question with regards to taking the logarithm of a variable (Statistics Question)
Say you have a bar graph displaying data for an example "Cost of Computer Orders by the Population" and you are ...
0
votes
1answer
39 views
interpreting an expression involving two random variables
Consider a function $$g=E[\max(a+X,d+Y)]$$ where $a,d\in R$ and $X$ and $Y$ are independent and identically distributed standardized random variables with mean $\mu$, variance $\sigma^2$, continuous ...
