A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense).

learn more… | top users | synonyms (1)

1
vote
0answers
14 views

How to decide which of two distributions a sample is from?

I have two random distributions. How can I get a quantitative estimate of the likelyhood that a particular sample was taken from one or the other of the distributions? To be more precise: Let $I = ...
1
vote
1answer
35 views

Exclude Some samples for calculating CDF

I am calculating the asymptotic cumulative distribution of $M_n = \max(X_1,X_2,\dots,X_N)$. My problem is $X_1,X_2,\dots X_p$ and $X_k,X_{k+1},\dots,X_N$ have non identical CDF for $p<<k$ and ...
1
vote
1answer
41 views

What is the expected number of coin flips, if you stop when the first coin flip is the same as the last?

In order to calculate the $\text{E}[X]$ where $X$ is the number of total coin flips, this is the approach I took: The probabilities are: $Pr(H) = p$ $Pr(T) = (1-p)$ Define indicator random ...
2
votes
2answers
41 views

Weakly correlated Random variables

If $N$ random variables are identically distributed but weakly correlated, in what condition we can approximate them as independent identically distributed (iid) ? I saw an old paper where based on ...
0
votes
1answer
17 views

How to compute $\mathbb{P}(A|B)$ of two independent RVs? [duplicate]

There are two independent RVs $X \sim \mathcal{U}(-1,5)$ and $Y \sim \mathcal U(-5,5)$. Let $A = \{ X \ge Y \land Y \ge -1 \land Y \le 1\}$ and $B = \{ X \le 1\}$. What is $\mathbb P (A | B)$? My ...
3
votes
1answer
75 views

Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$

Given two independent random variables $X \sim \mathcal{U}[-1,5]$ and $Y \sim \mathcal{U}[-5,5]$, what is $$\mathbb{E}\{Y - X | X \le 1, Y > X, Y \in [-1,1] \}\,?$$ I managed to compute the ...
0
votes
1answer
26 views

Multiplication of two random distribution

I am trying to find the resulting PDF , when two random functions are multiplied. First function obeys normal distribution and second function obeys cauchy distribution. Can anybody tell me how to ...
0
votes
1answer
114 views

What is the correlation between X and X+Y?

If $X$ and $Y$ are two random variables, how do I calculate the correlation of $X$ and $X+Y$ in terms of $\rho$, $σ_x^2$ and $σ_y^2$ given that the $\text{Variance}(X)= σ_x^2$ and ...
3
votes
2answers
95 views

What is the meaning of the conditional $y|b$

I think I'm confused about a very simple thing. When we say that some variable is distributed as a Poisson distribution and we write $y \sim \text{Pois}(\lambda)$, is this the same that saying ...
-1
votes
2answers
44 views

Example of a random variable that is not iid

What is an example of a random variable that is not i.i.d? The usual ones (coin flips, rolling of a dice) are all i.i.d, so I am trying to understand what is an example of a random variable that is ...
4
votes
1answer
92 views

(Co)variance of product of a random scalar and a random vector

Given a random scalar $ x \in \mathbb{R} $ and a random vector $ Y \in \mathbb{R}^n $ that are independent, can it be said that: $$ {\rm cov}(xY) = {\rm var}(x){\rm cov}(Y) + {\rm var}(x)E[Y]E[Y]^T + ...
2
votes
2answers
60 views

How to compute $\mathbb{P}(3x > -y > x \land x > 0 \land y < 0)$? [duplicate]

Knowing that both $x \sim \mathcal{N}(0,1)$ and $y \sim \mathcal{N}(0,1)$ ($x,y$ independent from each other), I want to compute $$\mathbb{P}(3x > -y > x \land x > 0 \land y < 0)$$ I'm ...
0
votes
1answer
69 views

pmf of random variable

There is a random variable that can take 3 values with the following probabilities: Pr(x=0) = 0.4 Pr(x=0.5) = 0.2 Pr(x=1)=0.4 How should i write the pmf of this ...
-1
votes
0answers
42 views

Central/limit theorem problem

Lets have a sum of 500 i.i.d. random variables. Each assumes values 0 with probability 0.3, 1 with probability 0.2 and 2 with probability 0.5. Find the smallest $m$ such that probability that the sum ...
1
vote
1answer
48 views

Correlation under transformation

Suppose i have a random vector $X=(X_1,X_2,...,X_k)^T$ where each $X_i$ has cdf denoted by $F_i$ . The correlation matrix of this multivariate distribution is $R_k$. Define ...
13
votes
3answers
316 views

Uniform random variable as sum of two random variables

Taken from Grimmet and Stirzaker: Show that it cannot be the case that $U=X+Y$ where $U$ is uniformly distributed on [0,1] and $X$ and $Y$ are independent and identically distributed. You should not ...
0
votes
0answers
16 views

Relation of distributions

I want to predict a distribution using multiple related distributions. One method is to use multiple regression (the model specification is that the dependent variable, yi is a combination of the ...
4
votes
1answer
58 views

Do these random variables satisfy Lindeberg's condition?

I have the followig sequences: $Pr(X_n=n)=Pr(X_n=-n)=0.5$ $Pr(X_n=2^{n/2})=Pr(X_n=-2^{n/2})=0.5$ I have to show whether they satisfy Lindeberg's condition or not, but this condition is a bit ...
1
vote
0answers
21 views

How to simulate a random variable from a matrix variate distribution?

I am trying to simulate a random variable from the matrix variate normal distribution but have not seen any literature on it. If somebody could point me in the right direction for that or if they ...
1
vote
2answers
50 views

Transform two correlated random variable to independent variables without knowing correlation

I am thinking about this interesting question which arises in the following realistic setting. For example, in one medical experiment one drug and one placebo are applied to two randomized groups of ...
0
votes
0answers
21 views

Fast way to compute central moments of a Poisson random variable?

I am looking for a way to quickly compute the central moments of a Poisson random variable. I've found a couple of resources on how to compute the central moments, but I'm still trying to figure out ...
1
vote
0answers
13 views

Decomposition of a random vector into uncorrelated components

I have a set of random vectors $Y_i$ and their correlation matrix $C_{i,j}$. Each vector can be thought of as a sum of two uncorrelated vectors $Y_i=A_iX+B_iY$, where $X,Y$ are the same vectors for ...
2
votes
1answer
25 views

Properties of the minimum of several random variables

I've come across an interesting problem in my research that I don't quite know the answer to. Suppose I have a bunch of random variables: $$ X_1, X_2, X_3, ... X_N $$ They are not identical but they ...
6
votes
1answer
90 views

Random variables with some properties (conditional expectation)

I am looking for two random variables which fulfills the following two things: a) $\mathbb E(X|Y)<\infty$ and $\mathbb E(Y|X)<\infty$ b) $E(X|Y)> Y$ and $\mathbb E(Y|X)>X$ a.s Here is ...
0
votes
0answers
39 views

Using lmer for random effect and nested interpreting model comparison

I'm trying to do a lmer in r. I did an experiment in which I manipulated the temperature. My dataframe contains the following factors: Site: 11 level, random Species: 2 levels, fixed Subject: 10, ...
0
votes
1answer
20 views

MSE decomposition to Variance an Bias Square

In showing that MSE can be decomposed into variance plus the square of Bias, the proof in wikipedia has a step, highlighted in the picture. How does this work? How is the expectation pushed in to the ...
2
votes
2answers
53 views

Derive the LLN for a certain sequence

I have a sequence of dependent random variables $X_1, X_2...X_n$. Each RV is correlated with two other RVs and uncorrelated with the others.The ones that are correlated satisfy the condition ...
1
vote
0answers
34 views

What is the distribution of these functions of Nakagami random variables?

I am new to this forum and hope I can get help. A Nakagami random variable $X$ with parameter $m$ has the following pdf $$X\sim \frac{2m^m}{\Gamma(m)\Omega^m} x^{2m-1}e^{-\frac{m}{\Omega}x^2}$$ ...
0
votes
1answer
13 views

Prevalence estimates based on randomized sample of clinical data

This is probably one of the more straight forward questions on here but here it is: I want to use a random number generator to sample X number of charts to look for the # occurrences of Y event. So ...
2
votes
0answers
24 views

asymptotic covariance between mean and standard deviation

I am trying to estimate the asymptotic covariance between mean and standard deviation. I know the following $$\sqrt n \hat \mu \xrightarrow{d}N\left( {\mu ,{\sigma ^2}} \right),\sqrt n \hat \sigma ...
0
votes
1answer
41 views

Example for uncorrelated, not independent , but with same distribution functions random variables

I am looking for an example of two random variables X and Y on $\Omega=\{-2,-1,0,1,2\}$ with the following properties: a) X and Y have the same distribution b) X and Y are uncorrelated c) X and Y ...
1
vote
0answers
74 views

Exponential random variable

The time it takes a printer to print a job is an exponential random variable with mean of 10 seconds. You send a job to the printer at 9:00 am, and it appears to be the fourth in line. What is the ...
3
votes
0answers
42 views

Sum of Bernoulli random variables

I need some help with a homework assignment. The question I'm given is: "Suppose that $X_1, X_2,..., X_n, W$ are independent random variables such that $X_i\sim Bin(1,0.4)$ and $P(W=i)=1/n$ for $i=1, ...
0
votes
1answer
67 views

How to bound a probability with Chernoff's inequality?

In my class, we were given Chernoff's inequality as $$P(X\le -t) \le e^{(-(\lambda*t - \log( E(e^{-\lambda*x}))))}$$ $$P(X\ge -t) \le e^{(-(\lambda*t - \log( E(e^{\lambda*x}))))}$$ It says that to ...
4
votes
2answers
82 views

Expectation of $(X + Y)^2$ where $X$ and $Y$ are independent Poisson random variables

I would really appreciate anyone's help with this problem: (let $E$ denote expectation) Suppose $X$ and $Y$ are independent Poisson random variables, each with mean $1$. Find: $E[(X + ...
0
votes
1answer
24 views

Sum of dependent R.V

I have two random variables whose PDF are parameterized by an unknown constant as follows: P(A;d) P(B;d) apparently, these two are not independent, so to find P(A+B;d) one cannot use convolution. ...
0
votes
1answer
46 views

sum of correlated random sample

Suppose I have 1000 draws each of two random variables X and Y. If I wanted to sample the sum of these variables, I would simply calculate 1000 samples, i.e. $$ S_{i}=X_{i}+Y_{i}, i=1,2,…,1000 $$ ...
0
votes
0answers
16 views

G and R matrices in mixed model and model selection

I have data in which the plants were subjected to four conditions and measured weekly for a month. I would like to incorporate "plot" as a random factor into my linear mixed model using SPSS. I am ...
0
votes
1answer
47 views

Covariance of a compound distribution

I am trying to find the covariance of a compound distribution. Given $X=x$, where $X \sim \mathrm{Uniform}(0,1)$, $Y$ is (conditionally) normally distributed with mean $x$ and variance $x^2$. I ...
0
votes
1answer
39 views

Bayesian Network

I am preparing for midterm exam and need to know what is the step by step solution to this question? Answer is shown in red. Also any external related link is very much appreciated.
1
vote
2answers
97 views

How to prove dependence of random variables

I need to solve the following problem. Let $X$ be a normal random variable with mean $\mu$ and standard deviation $\sigma$ and let $I$, independent of $X$, be such that $\mathbb{P}(I = 2) = ...
0
votes
0answers
16 views

Convergence of Random Variables meaning

What is the intuitive explanation of convergence of random variables? what is meant by saying that a sequence of random variables CONVERGE?
1
vote
1answer
28 views

Sequence of Random Variables

I am confused about how to approach sequence of random variables that are not identically distributed. For example, consider a sequence $X_1, X_2, \dots, X_n$ with the pdf: $$ f(X_n)= \begin{cases} ...
1
vote
0answers
27 views

Sampling from a distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Normally when simulating the process with the ...
1
vote
0answers
23 views

Number of trials to observe all values of a uniform discrete random variable X with a probability of at least 1-q?

Let X take on p values with equal probability. If n trials are to be conducted to ensure that the probability of not observing any of these p values is less than or equal to q, what is the value of ...
0
votes
0answers
20 views

Linear Combination of Random Normal Variables

In order to prove that the linear combination of two independent normal distributions(say Z=X+Y) is normal, i am using their MGFs to show that the linear combination also has a similar mgf. This works ...
1
vote
0answers
42 views

Distribution for $Y = \sqrt{X_1^2 + X_2^2}$, when $X_1, X_2$ are dependent and normally distributed with different variance? [duplicate]

Is there a closed form distribution for the transformation given by $Y = \sqrt{X_1^2 + X_2^2}$, when $X_1, X_2$ are jointly normal but dependent random variables with different variance? OBS: I know, ...
2
votes
1answer
69 views

Combination of Random Variables Conditional Probability

If A and B are independent discrete random variables and C = A+B, then how should one compute the pmf of P(A|C)? For example, let X be the result from a coin toss(1 or 0 for H and T) and Y be the ...
1
vote
1answer
39 views

Probability distribution, unfair coin

An unfair coin which has 0.35 probability to result head is tossed four times. Build and represent graphically the probability distribution and the cumulative ...
2
votes
0answers
37 views

Are matrix Fisher r.v.s closed under multiplication?

With appropriate parameters, a matrix Fisher distribution provides a distribution over SO(3) (i.e. over rotations in $R^3$). See this MathOverflow post for a few notes describing the distribution. ...