The random-variable tag has no wiki summary.
2
votes
1answer
28 views
How to prove independentness of marginal/conditional (?) posterior distributions?
This is a question about exercises 4.2 and 4.3 of Jim Albert’s “Bayesian Comptutation With R” (p. 82). Note that while this might be homework, in my case it is not.
We are to prove that, given two ...
0
votes
0answers
16 views
Random variables resulting due to single or multiple experiments
Assume there are ‘n’ entities that collect some data after each ‘t’ time instances. Generally their collected data is within an “expected” range. However, occasionally the data exceeds the “expected” ...
0
votes
1answer
47 views
What is the Mean and Standard Deviation of the division of two random variables? [duplicate]
I have two normally-distributed independent random variables X and Y and I need to calculate its division Z.
As far as I understand the mean of Z is $\mu_Z = \frac{\mu_X}{\mu_Y}$, but I don't know ...
0
votes
1answer
70 views
Can I derive the PDF ( f(C) ) from a spatial function defined as C(x)?
Say I have a random variable (such as concentration) that is defined spatially by some function $C(x)$.
I would like to derive a PDF $(f(C))$ from the concentration function $C(x)$ over some domain ...
0
votes
1answer
52 views
Show that $G(x)$ is a distribution function and find mean
Let $F$ be a distribution function on $\mathbb{R}$ with $F(0)=1$ and $\mu$ be its mean.Show that $$G(x)=\frac{1}{\mu}\int_{0}^{x}[1-F(t)]dt$$ is a distribution function. Also find its mean.
...
3
votes
1answer
64 views
Expected value and variance of log(a)
I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
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 ...
1
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0answers
23 views
Interpretation of main effect when interaction term being significant (ex. lme)
As an example I use "Pinheiro, J. C. & Bates, D. M. 2000. Mixed-effects models in S and S-PLUS. Springer, New York." page 225, where rats are fed by 3 different diets over time, which body mass ...
2
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1answer
65 views
The sample size applied to a non-normal distribution
I have a single variable that represents my population values (sample of data):
...
2
votes
1answer
74 views
Cosine of a uniform random variable
I have to find pdf of Y = cosine(X) where X is a random variable distributed uniformly in [-pi,pi]. I solved this using distribution function method, and the result was:
$f_{Y}(y) = \dfrac{1}{\pi ...
1
vote
1answer
74 views
How to calculate minimum of multiple exponential distributions?
$X_1$, $X_2$, $X_3$ are independent random variables, each with an exponential distribution, but with means of $2.0, 5.0, 10.0$ respectively. Let $Y$= the smallest or minimum value of these three ...
2
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0answers
29 views
Comparing divergence from uniform distributions with differing supports (discrete)
Imagine we have a potentially biased coin and a potentially biased six-sided die and we want to know which is more biased than the other.
Firstly, is this a reasonable goal? Could it make sense to ...
0
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0answers
45 views
Proof that a and b in linear regression are random variables
I had posted this question http://math.stackexchange.com/questions/353703/proof-that-a-and-b-in-linear-regression-are-random-variables in math.stackexchange.com but I am certain that the reason why I ...
0
votes
0answers
15 views
Can Kalman filter apply to distribution function?
The standard Kalman filter uses a series of measurements observed over time, to decomposite the signal and noise.
However, when I'm modeling the distribution (pdf or cdf) of a variant, is there a ...
0
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0answers
61 views
Draw conditioned beta distributed random variables
I am trying to draw a beta distributed random variable (recovery rate), conditioned on another beta distributed random variable (default rate).
I have shape parameters $(\alpha= 0.6, \beta = 55.5)$ ...
1
vote
1answer
80 views
Standard deviation of weighted sums of random distributions with weights random but fixed
Let $a,b,c,d$ be independent normally distributed random variables. I'm aware that the following distributions:
$$c a + d b$$
$$(c+d)a$$
both have the same standard deviation ($=\sqrt{2}$ if ...
0
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0answers
16 views
Why is the CDF of the maximum of two random variables their respective CDF's multiplied? [duplicate]
I have the following random variables:
X = uniform over [0, 1]
Y = uniform over [0, 1]
Z = max{X, Y}
(X and Y are independent)
I don't understand why the CDF of ...
0
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0answers
103 views
two way repeated measures anova random factors missing data
I have a pretty simple time series experiment that I'd like to analyze in R. I have an experimental and control group and for each individual in each group I collected samples from them over a course ...
1
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2answers
85 views
Constant hazard in survival analysis and random event occurence
I read that in survival analysis, when the hazard function $$\lambda(t)=\underset { dt\rightarrow 0 }{ lim } \frac { Pr(t\le T<t+dt|T\ge t) }{ dt } =c$$ then the event occurrence is random and ...
24
votes
3answers
769 views
Why does the correlation coefficient between X and X-Y random variables tend to be 0.7
Taken from Practical Statistics for Medical Research where Douglas Altman writes in page 285:
"...for any two quantities X and Y, X will be correlated with X-Y. Indeed, even if X and Y are samples ...
2
votes
1answer
168 views
How to use Box-Muller transform to generate n-dimensional normal random variables
I'm trying to generate random variables. I read about Box-Muller transform which is a way to generate a pair of normal variables, 2-d normal distrubution. But how do I expand that transform to ...
1
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2answers
389 views
Determine density of min(x,y) and max(x,y) for independently uniform distributed variables
Two independent random variables, X and Y, are uniformly distributed on the unit interval (-1,1).
Determine the density for U=min(X,Y) and for W=max(X,Y)
2
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0answers
25 views
Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix
I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
0
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5answers
183 views
How can I find distribution from mean and variance
If I know the mean and variance of a discrete random variable $\in \{0,1,\dots \}$, How can I find the distribution?
0
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2answers
130 views
How to compute the PDF of a sum of a discrete and a continuous random variable? [closed]
I have a problem with this exercise in probability and statistics:
Calculate the probability density function (PDF) of
$$Z=X+Y$$
where $Y$ is discrete random variable which is equal to $-1$ and $1$ ...
3
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0answers
25 views
Multidimensional scaling of random matrix
Suppose I have a random symmetric matrix W of size $n\times n$, with i.i.d. coefficients uniformly distributed in [0,1], and I set $W_{ii} = 0$.
Then I apply a Multidimensional Scaling of dimension ...
3
votes
1answer
227 views
How to create a random variables in a simulation using skewness and kurtosis as well as average and standard deviation input?
I am curious to learn whether there are any best practises in creating random variables for a Monte Carlo simulation using input such as skewness and kurtosis information of a particular distribution. ...
1
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0answers
37 views
How can I perform transformations on vector-valued random variables?
I'm trying to find a way to compute presence/absence probabilities over random vectors that contain sequences of values rather then presence/absence indicators. Suppose I have a set $S$ of possible ...
3
votes
2answers
241 views
Conditional expectation of exponential random variable
For a random variable $X\sim \text{Exp}(\lambda)$ ($\mathbb{E}[X] = \frac{1}{\lambda}$) I feel intuitively that $\mathbb{E}[X|X > x]$ should equal $x + \mathbb{E}[X]$ since by the memoryless ...
2
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0answers
308 views
How to find marginal distribution from joint distribution with multi-variable dependence?
One of the problems in my textbook is posed as follows. A two-dimensional stochastic continuous vector has the following density function:
$$
f_{X,Y}(x,y)=
\begin{cases}
15xy^2 & \text{if 0 < ...
1
vote
1answer
48 views
Does this break down adding independent probabilities?
I was thinking about this today so I decided to ask it here. I know the rule of adding probabilities. As I was taught in grade school "OR" typically means add and "AND" typically means multiply.
...
2
votes
1answer
201 views
Derivation of Rayleigh-distributed random variable
I only have a uniform distribution function between [0,1]. And from this distribution, I should generate a sequence of Rayleigh distributed random variable using some software.
Anyhow, I was able to ...
4
votes
2answers
259 views
Covariance of transformed random variables
I have two random variables $X > 0$ and $Y > 0$.
Given that I can estimate $$\text{Cov}(X, Y),$$ how can I estimate $$\text{Cov}(\log(X), \log(Y))?$$
2
votes
1answer
247 views
Expected value of modified geometric distribution
I am trying to find the expected value of $X$, where $X$ is the number of orders a customer will make in a lifetime.
Assuming that there is a $p=.1$ chance of the customer placing an initial order, ...
4
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1answer
117 views
What can we conclude about the distribution of the sum of two random variables?
If we know, for independent random variables $X$ and $Y$,
$P(X>x)\leq0.05$, and $P(Y>y)\leq0.05$, can we say anything about $P(X+Y>x+y)$? Can we be certain that it is less than $0.05$? Under ...
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0answers
20 views
How to stabilize features over time?
I have in my model some features, which seem to have some super power to explain the training data. To be more specific, the model is to predict clicks and the features are the ...
5
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0answers
276 views
pdf of the product of two independent random variables, normal and chi-square
what is the pdf of the product of two independent random variables X and Y, if X and Y are independent?
X is normal distributed and Y is chi-square distributed.
Z = XY
if $X$ has normal distribution ...
4
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0answers
81 views
About tail distribution of a sum
Do we know anything about the tail distribution of sum of squares of a limited number of i.i.d exponentially distributed random variables? I'm looking for a good bound.
1
vote
1answer
79 views
How do I prepare data which has a trend for use in a Copula model?
I want to use a set of daily water quality data including 3 parameters in a Copula model. Somebody told me these data do not have a condition of a random variable to use in copula, and I should do ...
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0answers
24 views
When are time averages equal to statistical averages?
I have a data set which comprises N measurements. Each measurement is an 8 dimensional vector representing 8 voltages measured from a machine. I want to compute the covariance matrix of this data. ...
4
votes
1answer
228 views
Expected value of a transformed random variable
I would be interested in computing the expected value of the following random variable $Y$.
Let $X$ be either a $\mathrm{Bin}(p,N)$ or a $\mathrm{Hyp}(n,m,N)$ with $m$ number of successes (I would ...
0
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1answer
38 views
Is computer network throughput an independent variable?
The central limit theorem assumes independent variables and I want to apply it to study the performances of my network speed (computer networks). What I have a is the throughput measurements of my ...
3
votes
2answers
178 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
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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 ?
...
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0answers
74 views
Conditional Entropy of linear combination of random variables
$X_1 \sim \mathcal{N}(0,P)$, $X_2 \sim \mathcal{N}(0,P)$ and $Z \sim \mathcal{N}(0,N)$ with $X_1,X_2,Z$ mutually independent.
How do we compute
$$
H(aX_1+bX_2+Z \mid \alpha X_1+\beta X_2)
$$
where ...
2
votes
1answer
128 views
Generating samples of correlated normally distributed variables with some of the variables pre-selected
I would greatly appreciate any of you who could help me with this challenge. I am going to state the problem in sequential order, so as to make it clear:
I have $n$ normally distributed random ...
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0answers
97 views
How do I apply the method of moments for estimating parameters in a sum-relationship?
We have a model relationship between three random variables like this:
$$ U = C + S $$
I have a ton of measurements of realizations of $U$, as well as a ton of realizations of $C$. But the ...
7
votes
3answers
95 views
What is the link between methods such as matching and statistically controlling for variables?
Often in research articles you read the researchers have controlled for certain variables. This can be done by methods such as matching, blocking, etc.
But I always thought controlling for variables ...
2
votes
1answer
140 views
Sum of normally distributed variables is a normally distributed variable?
Consider two Wiener processes:
$$
\begin{aligned}
X_a &\sim\mathcal N(0,a) \\
X_{a-b} &\sim\mathcal N(0,a-b)
\end{aligned}
$$
How do I show that:
$$
X_a - X_{a-b} \sim\mathcal N(.,.)
$$
That ...
3
votes
1answer
177 views
Experimentially proving that random variables are independent
I just had a very simple (possibly very dumb) question.
How would I, experimentally prove that two random variables drawn either from the same population or two different populations are independent ...
