Tagged Questions
1
vote
0answers
26 views
P.d.f of a discrete fourier transform of binary variables
Let $\{a_n\}$ be a set of $N$ "binary" random variables uniformly distribuited in $\{-1,1\}$.
The discrete fourier transform is defined
$b_k=\frac{1}{\sqrt{N}}\sum_{n=0}^{N-1} a_n e^{-2 \pi i k n ...
4
votes
2answers
62 views
Central Limit Theorem. How to apply to the task.
The research showed that the probabilities of 3, 4, 5, 6 and 7 cars broken on one day are 0.3, 0.4, 0.2, 0.08, 0.02 respectively. If 221 car broke in 50 days, does it show that more cars break than ...
1
vote
1answer
35 views
Simple question on random variables and statistics
Let X1 and X2 be 2 random variables. X1 = 20. X2 = 30. Each of those has a standard deviation of 5.
If the random variables were normally distributed, what is the probability of getting such a ...
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 ...
5
votes
0answers
64 views
What is the distribution of $\sqrt{X^2+Y^2}$ when $X$ and $Y$ are Gaussian but correlated?
If $Z = \sqrt{X^2+Y^2}$, and $X$ and $Y$ are zero-mean i.i.d. normally-distributed random variables, then $Z$ is Rayleigh distributed.
What is the distribution of $Z$ if $X$ and $Y$ are correlated ...
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
18 views
Is $f_{\Theta|Z}(\theta|z)$ Gaussian when $Z = \theta^3 + V$, and given that $\Theta$ and $V$ are Gaussian?
$\Theta$ and $V$ are zero mean Gaussian random variables with variances $\sigma_\Theta^2$ and $\sigma_V^2$.
A third random variable $Z$ is defined as:
$$
Z = \Theta^3 + V
$$
Is ...
0
votes
0answers
48 views
How to prove that $Y=\ln(X)$ approximately Normal when $X$ is a Normal random variable with $\mu\gg\sigma$
I wanted to prove that PDF of $Y=\ln(X)$ tends to a Normal distribution with $\mathcal{N}(\ln(\mu_{x}),\sigma^{2}_{y})$ when $X\sim\mathcal{N}(\mu_{x},\sigma^{2}_{x})$. It is also important to note ...
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
32 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
73 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
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 ...
1
vote
1answer
66 views
Mean and Variance Convergence with r.v.
Let $(X_n)_{n\ge 1}$ be a sequence of random variables, with respective distributions being Gaussian, with respective mean $\mu_n \in \mathbb R$ and variance
$\sigma_n^2 > 0$. Prove that if $X_n$ ...
1
vote
1answer
60 views
Linear transformation applied to a multivariate Gaussian random variable - what is the mean vector and covariance matrix of the new variable?
Given a random vector $\mathbf x \sim N(\mathbf{\bar x}, \mathbf{C_x})$ with normal distribution. $\mathbf{\bar x}$ is the mean value vector and $\mathbf{C_x}$ is the covariance matrix of ...
0
votes
1answer
73 views
Weibull Distribution question
Not sure how to approach this one, some help would be appreciated.
It has been observed that 5% of the students who take a certain exam will finish in less than 20 minutes and 95% will finish in ...
1
vote
4answers
253 views
The sum of n independent normal random variables.
How can I prove that the sum of $X_1, X_2, \ldots,X_n$ random variables, all of which have normal distributions $N(\mu_i, \sigma_i)$, is a random variable that is itself normally distributed with mean ...
0
votes
2answers
53 views
Distribution of two joint normal random variables
If two random variable $u_1$ and $u_2$ have a joint normal distribution what will be the distribution of the random variable $u_1-u_2$?
0
votes
1answer
189 views
Cumulative distribution function determine the random variable
I don't know that determine is the right word, but I try to explain. What I need to understand. :) So..
We know's that if a function fit this conditions:
Monotonically non-decreasing for each of its ...
0
votes
0answers
36 views
$\phi$ mixing for Gaussian process
I have a Gaussian random process(LTI filtered white noise) and I have to prove that it is $\phi$ mixing.
I tried to take the direct approach by taking the joint pdf of $x_s,x_{t+s}$ and find the ...
