Tagged Questions

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

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3
votes
1answer
15 views

Interesting Probability Question - Birthday Problem Variation

Suppose at a hipster eatery they make craft pickles. At this eatery they have n pickle makers (picklers). Every day each pickler makes 10 jars of pickles. Whenever any pickler has a birthday, there is ...
2
votes
2answers
35 views

The bug “probably” gets stuck!

Consider a regular tetrahedron with vertices $A,B,C,D$. A bug starts crawling from $A$. The bug moves from one vertex to the other along the edges continuously until it reaches $D$, where there is ...
0
votes
1answer
10 views

Expected Min/Max when picking numbers between 0 and 1

Suppose you pick two numbers between $0$ and $1$ with each number being picked at equal probability. What is the expected min/max of these two numbers? What if you picked ten numbers from $0$ to $1$? ...
1
vote
1answer
7 views

Assistance please on distribution problems

How many ordered quadruples (a,b,c,d) satisfy a+b+c+d=18, where a,b,c,d are odd positive integers? How many ordered quadruples (a,b,c,d) satisfy a+b+c+d=18, where a,b,c,d are integers such that ...
0
votes
0answers
13 views

CDF to Borel measure

If I have a right-continuous nondecreasing function $F:\mathbb{R} \to (0,1)$ that tends to $0$ and $1$ as $x$ tends to $-\infty$ and $\infty$ respectively, does $F$ necessarily induce a Borel measure ...
4
votes
1answer
27 views

Distribution of functions of uniform random variables

Given these two independent and uniform distributed random variables, $$X \sim U[-\pi,\pi]$$ and $$Y \sim U[-\pi,\pi]$$ What is the distribution of $$\sin(X)$$ and $$\sin (Y)$$ and the distribution ...
0
votes
1answer
6 views

Calculating the distribution, expected value and variance

I have no idea how to solve the following problem. Could someone give me some pointers on how the solve the following problem? Choose a random country. Taken $n$ persons from this country. ...
0
votes
0answers
14 views

Is the distribution of square of the sum of Nakagami random variables the same as the sum of Nakagami RV squared?

Having random variable $U_i$ Nakagami distributed with parameter $m$, for $i\in\{1,n\}$. What would the distribution of the following two examples be $$ \big|\sum_i {a_i U_i}\big|^2$$ where $a_i$ ...
0
votes
1answer
18 views

Almost a Frechet distribution but not quite yet

I have function as $$\frac{2}{\alpha}x^{\frac{2}{\alpha}-1}e ^{-x^{\frac{1}{\alpha}}}$$ This kind of reminds me of the Weibull and Frechet distribution but not quite because if it were I should be ...
1
vote
0answers
6 views

Random graphs: A random graph induces a distribution on each link. Do they uniquely determine the graph?

Let $G$ be a random graph with $n$ nodes, with the nodes numbered. $G$ induces a distribution in the set of all graphs of $n$ nodes and we can identify this distribution with $G$. Given the nodes ...
1
vote
2answers
33 views

Is the y axis on a PDF actually meaningless?

This idea popped in my head when I was reading this post on the normal distribution and the y-axis. My question is (and taking advantage of a nearby computer), a PDF inputs one value and returns ...
0
votes
1answer
20 views

What is the joint distribution of sample mean and sample variance of normal distribution?

${X_i} \sim N\left( {\mu ,{\sigma ^2}} \right)$, define $\overline X =\dfrac{1}{{n}} \sum\limits_{i = 1}^n {{X_i}} $, ${S^2} = \dfrac{1}{{n - 1}}\sum\limits_{n = 1}^n {{{\left( {{X_i} - \overline X} ...
0
votes
0answers
4 views

How to determine how likely it is for a data point to belong to each of two [normal] distributions?

How do I determine the likelihood of a data point to belong to a distribution? Context I have a set of data, which has the following histogram: I would like to analyze each of the data points in ...
0
votes
0answers
23 views

Meaningful statistic measure of data pairs

I have a dilemma. I have pairwise data, (a,b), that represents some form of speed, whether it's miles/hour or megabits/second. Let's say that we have the following set of data from measuring the ...
2
votes
2answers
123 views

Probability (X >Y) when X and Y have the same distribution?

This is a problem from HW4 Joe Blitzstein's Harvard Stat 110 course. Let X be a random day of the week, coded so that Monday is 1, Tuesday is 2, etc. (so X takes values 1, 2, . . . , 7, with equal ...
1
vote
1answer
23 views

How to find the $E(N)$ using $E(M)$ where the $M$ and $N$ follow slightly different scenarios

An author sends his first manuscript to a large number of publishers, $C, D, E, ...$ , in turn, only approaching each one, after the first, if the one before has refused it. There is a constant ...
0
votes
0answers
7 views

Mix of two bivariate distributions (two correlations hidden in data)

We have two sample vectors $X$ and $Y$ which are realizations (observations) of metric (continuous) random variables, and are interested in a sample correlation between them. Actually, a correlation ...
1
vote
1answer
19 views

Equal in distribution but unequal almost everywhere?

If this question has been asked, I apologize but I could not find it. I was wondering if it was possible construct $X$, $Y$ two iid rv's such that they equal in distribution, i.e. $P_X(B) = ...
1
vote
0answers
22 views

Computing a Finite Expectation

Assume $1\leq\ k<m<n$ are positive integers and $X_1,X_2,...X_n$ are i.i.d. Geometric($p$) random variables. For all $j\geq\ k$ define $I_j=[(i_1,i_2,...,i_k):1\leq\ ...
0
votes
0answers
8 views

Sum of Lomax random variables

Suppose $X_1,X_2,\cdots X_n$ are $n$ i.i.d Lomax random variables with pdf $f(x)=\frac{m}{(1+x)^{m+1}},x\geq 0,m\in \mathbb N$. I need to determine the pdf (or cdf) of the sum $S_n=\sum_{i=1}^{n}X_i$. ...
1
vote
0answers
20 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
votes
1answer
24 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
vote
0answers
3 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
votes
0answers
20 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
18 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
votes
3answers
25 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 ...
0
votes
2answers
25 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 ...
0
votes
2answers
23 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 ...
1
vote
2answers
38 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 πœŽπ‘‹ 2 = 1, πœŽπ‘Œ 2 = 2 . Find the pdf of the random variable Z=|X+2Y| and from it compute the mean and variance of Z ...
0
votes
0answers
23 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
vote
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
vote
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 ...
-2
votes
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?
0
votes
0answers
14 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
36 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
25 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
votes
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
votes
0answers
91 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
28 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
20 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 $E[X]-E[x]=\frac{1}{\lambda}-x$.
-1
votes
1answer
36 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
66 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
vote
0answers
44 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 ...