Tagged Questions

Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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0
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0answers
7 views

For fun, how many paths are there in a flow matrix?

I just got done doing the whole flow-matrix percolation exercise in programming. That is a situation where you have, for simplicity, an $n\times n$ grid of 0s and 1s. 0s represent blocked sites and ...
0
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1answer
12 views

Probability from multiple trials

This questions is from a practice mid-term that I don't have a solution to. A monkey in a research lab is given 6 tiles with the letters AAABNN. On each trial the monkey randomly arranges the ...
1
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0answers
2 views

Why the doubly non-central F distribution does not have a mean or variance if the denominator degree of freedom is less than or equal 2 ??

Normally the doubly non-central F distribution is generated by the division of two non-central chi squared Random Variables,, so what is the the problem of using any famous formula to get the mean of ...
0
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0answers
15 views

Lack of memory of a geometric distribution, proving a general case.

I have to prove this for a general value so $P(X > j+k | X>j) = P(X > k)$ Using the conditional probability I get that $P(X > j+k | X>j) = \dfrac{P(X > j+k) \wedge P(X > ...
1
vote
1answer
17 views

What is the probability of success?

If I have 12 Possible questions, of which 5 are asked and I only need to answer 2 of them, what is the probability of my success (i.e., I am able to answer 2 of the 5 asked questions) if I learn 2 of ...
2
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3answers
14 views

Symmetric Distribution of Random Variable

Prove: Let $X$ and $Y$ be random variables with the same distribution. If $X$ and $Y$ take only two values​​, then $X - Y$ are symmetrically distributed around zero. Note: 1 - You can use ...
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2answers
22 views

Conditional Probability - chance for an event to happen

I am learning probabilities at the moment and I have come across this problem: A person takes four tests in succession. The probability of his passing the first test is p, that of his passing each ...
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2answers
16 views

Probability CDF question on highest number of marbles pulled out

I'm kinda stuck on this problem. Here goes: An urn contains n marbles, numbered 1, 2, . . . , n. Suppose k < n marbles are drawn from it at random without replacement. Let X denote the highest ...
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2answers
30 views

A random variable $X$ uniformly distributed over the interval $[0, 2\pi]$

A random variable $X$ distributed over the interval $[0, 2\pi]$ a) the pdf of $X$ b) the cdf of $X$ c) $P(\frac{\pi}{6} \leq X \leq \frac{\pi}{2})$ d) $P(-\frac{\pi}{6} \leq X \leq \frac{\pi}{2})$ ...
-1
votes
1answer
9 views

ranndom process and probabiity [on hold]

Let X and Y be two independent zero mean Gaussian random variables with variances 𝜎𝑋 2 = 1, 𝜎𝑌 2 = 2 . Find the pdf of the random variable Z=|X+2Y| and from it compute the mean and variance of Z ...
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0answers
18 views

Poisson Distribution word problems

During rush hour the number of cars passing through a particular intersection23 has a Poisson distribution with an average of 540 per hour. (a) Find the probability there are 11 cars in a 30 second ...
1
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3answers
38 views

Find the pdf of T = X + Y

Let (X,Y) be a random point chosen uniformly on region R = {(x,y) : |x| + |y| <= 1}. I need to find the pdf of T = X + Y. I know the joint density is just equal to 1/(area) = fxy(x,y) = 1/2 for ...
1
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0answers
34 views

Probability Distribution for a Weird Card Game

I promise this is not for a homework problem, even though this sounds like only something a professor would dream up. Here is the game: I begin with a deck of 13 cards: 1 through 10, Jack, Queen, and ...
1
vote
0answers
22 views

Gaussian random vector with 0 mean [duplicate]

Let $X =(X_1,X_2,X_3,X_4)$ be a Gaussian Random Vector with $\mathsf E(X_1)=\mathsf E(X_2)=\mathsf E(X_3)=\mathsf E(X_4)=0$. Show that $$ \mathsf E(X_1 X_2 X_3 X_4) = \mathsf ...
2
votes
1answer
12 views

How is this Variance found in this old question?

On this question: Probability: Normal Distribution they find these values: $\hat\mu = .05(150) = 7.5\space,\hat\sigma = \sqrt{150(.05)(.95)} = 2.67$ I see how they got $\mu$, but how did they get ...
-1
votes
0answers
18 views

Lottery Ticket Probability [on hold]

At a certain retailer, purchases of lottery tickets in the final 10 minutes of sale before a draw follow a Poisson distribution with mean = 15 if the top prize is less than 10,000,000 and follow a ...
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0answers
10 views

Random Sample taken [on hold]

A random sample of 300 people are taken. What is the probability that at least 100 of them are over 180cm in height given average height = 175 and standard deviation = 10?
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0answers
12 views

Right continuity of right inverse of right continous map

I am stuck on the following proof that I found in Dellacherie-Meyer's book "Probabilities and potential B", p. 119 (increasing processes and projectors). Given a map $a$ on $[0,\infty [$ which is ...
2
votes
1answer
11 views

distribution of $\|P_VX\|^2$ with orthogonal projection $P$ onto $V$

We've had the following question discussed today but without any result: Let $X_1,\dots,X_d$ be random variables, iid and $X_n\sim N(\mu_n,1)$. How can we describe the distribution of $\|P_VX\|^2$ ...
1
vote
2answers
33 views

Can 2 different random variables have the same CDF?

I'm looking for proof that two different random variables can have the same Cumulative Distribution Function; in other words, I'd like to disprove that a CDF uniquely defines a random variable. ...
0
votes
2answers
24 views

Co-relation Coefficient

$X$ and $Y$ are jointly continuous random variables. Their probability density function is: $$f(x,y) = \begin{cases}2x & \mbox{if } x\in [0,1], y\in[0,1] \\ 0 & \mbox{ otherwise ...
2
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1answer
23 views

Exponential distribution - maximum earthquake magnitude

Suppose $n$ earthquakes occur, and suppose the magnitude of earthquakes are independent and have an exponential distribution with mean $1$. What is the pdf of the maximum earthquake magnitude?
4
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0answers
87 views

How to compute or simplify this nasty integration?

Any hints on solving an integration of the following form, $$\int_{x}^{+\infty}\left(1-\frac{1}{1+sy^{-1}}\right) \left(\text{exp}(-\sqrt{y})+ y^{-\frac{1}{2}}(1-\text{exp}(-\sqrt[4]y)\right)dy $$ ...
1
vote
1answer
27 views

Joint probability density function probability

$X$ and $Y$ are jointly continuous random variables. $$f(x,y)=\begin{cases}kx & x\in[0,1], y\in [0,1]\\0 & :\text{otherwise}\end{cases}$$ a) What value of $k$ makes this a density ...
0
votes
1answer
19 views

Represent probability with multiple distributions. Archer shooting bullseyes problem.

The goal is to come up with two ways to represent this probability: An archer shoots a bulls-eye with probability $0.4$. If the archer shoots ten arrows, what's the probability that at least 3 are ...
2
votes
1answer
34 views

Find the value of k which makes f a density function.

Observe the following probability density function for a continuous random variable X $$f (x) = \begin{cases} k\sqrt x (1-x) &\text{ for }x\in(0,1)\\ 0 &\text{ otherwise} \end{cases} $$ Find ...
2
votes
2answers
21 views

Expected value of X-x for exponential distribution

Assume $X\sim$ exponential$(\lambda)$. In class we noted that $E[X-x|X\geq x]=\frac{1}{\lambda}$. Why is this? I would have thought that $E[X]-E[x]=\frac{1}{\lambda}-x$.
0
votes
1answer
31 views

Drawing Probability Density Function

Can someone help me to draw this pdf? I really don't have an idea how to convert a function to pdf. Thank you p(x | c) = 1/3 for 1 <= x <= 4 and P(c) = 0.5
3
votes
2answers
65 views

Normal Distribution and Cofffee

For my homework I have this question: A coffee vending machine automatically pours different types of coffee into cups. The amount of coffee dispensed is modeled by a normal distribution with mean ...
1
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0answers
40 views

Probabilty Models and distribution techniques

Coliform bacteria are distributed randomly and uniformly throughout river water at the average concentration of one per twenty cubic centimeters of water. Part (c) In testing for the concentration ...
1
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2answers
25 views

For Continuous RVs $X$ and $Y$ if $Y=$ “the CDF of $X$ evaluated in $X$” why does that mean $Y$ is uniform over (0,1)?

Let $X$ be a continuous random variable with CDF $F$. Define the random variable $Y=F(X)$, show that $Y$ is uniformly distributed over $(0,1)$. I have literally no idea why this would even be ...
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0answers
22 views

Questions dealing with Poisson distribution technique

"A waste disposal company averages 6.5 spills of toxic waste per month. Assume spills occur randomly at a uniform rate, and independently of each other, with a negligible chance of 2 or more occurring ...
1
vote
2answers
29 views

Compute the mean and variance given a probability mass function

I'm given the formula: $$(1-p)^{x-1}p, x = 1, 2, \ldots, \infty$$ and I'm asked to find the mean and variance. I know the mean is represented by $\sum_{i=1}^n p_ix_i$ and the variance by ...
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1answer
24 views

Discrete random variables and probability models

During jury selection a large number of people are asked to be present, then persons are selected one by one in a random order until the required number of jurors has been chosen. Because the ...
1
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2answers
43 views

Determining the Probability Distrubitive Function

A coffee chain claims that you have a 1 in 9 chance of winning a prize on their “roll up the edge” promotion, where you roll up the edge of your paper cup to see if you win. If so, what is the ...
0
votes
1answer
19 views

Random Distance on Torus

Let $U=(X_U, Y_U)$ and $V=(X_V, Y_V)$ be two independent random points in $[0,1] \times [0,1]$, where each possible position is equally likely. Now I am interested in the probability that these two ...
0
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1answer
24 views

Statıstıc problem

Will I use binomial distribution for this question? Can you help me please thnk you
0
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0answers
16 views

Is the first partial derivative of the cumulative joint density function equal to the marginal density

Is the first partial derivative of the cumulative joint density function $F(X,Y)$ equal to the marginal density? That is, is $\partial F(X,Y)/\partial X = f(X)$? What's the second partial derivative ...
0
votes
1answer
30 views

Probability Mass fuction for scratch ticket

A lottery ticket has 4 squares, each with either a star or an X. The printer printing these tickets has a 20% chance of printing a star per individual square. If the amount paid per star is as ...
0
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0answers
18 views

Statistic problem

Can you help me to solve this problem pls,I have exam and I am studyıng. What wıll I use, bınomial or Other thing ? Thank you
0
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2answers
21 views

Statistic binomial dist

Can you help me to solve this question pls, I consider that I Will use binomial distrıbutıon but I couldnt
0
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0answers
24 views

Inequality of gamma distribution

Let $X_{\alpha} \sim \text{Gammma}(\alpha,1),\alpha >0$ with distribution function $G_{\alpha}$ and $X_{\beta} <_{(c)} X_{\alpha}\,\forall ~0<\alpha<\beta<\infty$. Then show ...
0
votes
0answers
14 views

Probability distribution vectors over a set $S$

Given a (discrete) set $S$, is there a standard notation for the set of all distribution vectors over $S$? That is a notation for the set $$\{X\in[0,1]^S\mid\sum_{s\in S}X_s = 1\}$$
1
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0answers
14 views

Rate of Convergence in CLT for IID random vectors with dependent entries

Okay, so suppose I've got a sequence of IID random vectors $X_{n}$, where the entries of each $X_{n}=(X_{n,1},\dots, X_{n,i})$ are dependent. The motivating example here is the multinomial ...
3
votes
1answer
23 views

find the moment generating function of a pdf

Let $X$ be a random variable with pdf $$f_x(x)=\frac{1}{2\sigma}e^\dfrac{-|x-\mu|}{\sigma}$$, $-\infty< x<\infty$, $-\infty< \mu<\infty$, and $\sigma>0$. I have to find the mgf of $X$?. ...
0
votes
0answers
8 views

How to model and plot non-stationary mean-valued data

What would be the best way to plot a distribution of the data whose mean is non stationary. For example: if I have a data series, say y = [100, 97.3, 95.2, 93.2, 91.1, 91.2, ... 0] which yields ...
0
votes
0answers
30 views

Covariance of two normally distributed random variables

$$X = \frac1N \sum_1^N d_icos\theta_i $$ $$Y = \frac1N \sum_1^N d_isin\theta_i $$ $$d_i \sim LN(m_i, \sigma^2) $$ (LN mean Log normal distribution, $m_i$ can be measured, actually function of ...
1
vote
1answer
16 views

Distribution of orthogonal projection onto $\{(x,\dots,x\}\subset \mathbb R^d$

Let $D:=\{(x,\dots,x)\mid x\in\mathbb R\}\subset\mathbb R^d$ and $X$ be a random variable and normally distributed $X\sim N(\mu,\sigma^2 E_d) $ with $\sigma\neq 0$, $\mu\in\mathbb R^d$ and $E_d$ the ...
1
vote
1answer
19 views

How to express combined discrete-continuous RVs in one pdf?

Let's say we have a random variable $X$ that behaves in two different ways where $X\sim$Bernoulli(1/3) AND $X\sim U(0,1)$. $X$ follows the Bernoulli distribution 25% of the time and the uniform ...
0
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0answers
14 views

Singular values of $A$, where elements of $A$ are dependent centered normals

Fix $n \in \mathbb{N}$ and let $v$ be a multivariate normal random vector $v \sim N(0,\Sigma \in \mathbb{R}^{n^{2} \times n^{2}})$. Note that $v$ has $n^{2}$ entries. Then, let $A$ be the $n \times ...