This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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5 views

Gaussian Process: Using partitions of a choleky decomposition solution for conditional deduction.

If I define a GP over observed values, $y$, of a sensor reading over time, $t$, as (for simplicity assuming discrete time series e.g lets say readings after every 5 mins) : $y=f(t)+\epsilon$ where ...
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4answers
44 views

Prove a Continuous Distribution Function is Uniformly Continuous

Let $F$ be the distribution function for a random variable $X$ and it is given that $F$ is continuous over the entire real line. Prove that $F$ is uniformly continuous over the real line. My ...
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1answer
38 views

What is the probability that 3 out of 6 people pick the same thing in a game of rock paper scissors?

Currently my guess for a solution is [(6C3 x 3) * (3C2 x 2)] / 3^6 = 360/729 First bracket is considering 3 out of the 6 people picking the same hand to throw out (i.e rock paper or scissors) and ...
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0answers
19 views

Can you simulate from a cantor distribution?

Has someone run across a method for generating random variates from a Cantor Distribution? It seems like its abstract definition prevents this. In essence, can one "invert" the Cantor Function?
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0answers
24 views

Independent events: probability [closed]

without looking, shawna picks a pair of socks from a drawer containing 3 red pairs, 2 blue pairs, and 4 black pairs. if she returns the first pair and picks a second pair without looking, what is the ...
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2answers
31 views

Number of 5 letter words with at least one double letter

How many 5 letter words have at least one double letter, i.e. two consecutive letters that are the same? Answer is: $26^5 – 26*25^4 = 1,725,126 $ But how can i solve? I don't understand. The book ...
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0answers
23 views

Counting the number of integer solutions to a simple equation [duplicate]

In the following equation with unknown integers $x_i$, $1 \leq i \leq N$, the sum of all those integers are $R$. A constraint is added to each integer such that $Min_i \leq x_i \leq Max_i$. The ...
4
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1answer
33 views

Prove that the probability of two event sets are equal

Consider this problem: Let $A_1, A_2,...$ be an arbitrary finite sequence of events. Let $B_1, B_2,...$ be another finite sequence of events defined as follows: $B_1 = A_1, B_2 = A^c_1 >\cap ...
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3answers
24 views

Probability permutations

I'm trying to do the following probability question involving, I think, the ''amended'' multiplication rule: A Jar contains 3 red and 5 black balls. What is the probability of drawing 2 red balls ...
-2
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0answers
29 views

If I have a 75% chance of winning . What is the probability of losing 4 in a row and also 5 in a row? [closed]

I need to work out the above problem. I have read a similar equation on the site somewhere but still I'm not confident I have grasped the maths . ...
0
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0answers
29 views

Estimate probability density function of being in a certain time interval

​You arrive at a bus stop in an unfamiliar part of town. Assume that buses arrive at the stop with an unknown (to you) distribution and wait in the bus stop for a few ​minutes. The wait time ...
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0answers
28 views

How many orders are possible? [closed]

If we have $6$ red cards and $8$ yellow cards. And we spread them one after one. how many possible orders do we have?
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1answer
42 views

Deriving the Doob Meyer decomposition of a Sub Martingale using Ito's

Given the standard brownian motion $(B_t)_{t\in\mathbf{R}_{+}}$ and defining the sub-m.g.: $$X_t =B^6_t+2t$$ I would like to derive its Doob-Meyer decomposition: [Sub-m.g.]= [increasing ...
1
vote
1answer
43 views

Expected value of prime lottery ticket

Below is a problem I think that I have solved correctly, but cannot seem to get the correct answer. Any help would be greatly appreciated. You pay $\$13.00$ for a ticket. When you buy a ticket, ...
1
vote
1answer
30 views

Conditional probability or Bayes' theorem

I'm trying to do a question in probability: ''we flip three coins'' ''What is the probability that the second coin landed tails, given that two coins (exactly) landed head?'' I have set out the ...
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0answers
15 views

Probability of helpdesk associate receiving 3 calls from same caller

Forgive my lack of knowing the lingo, but I'm curious as to how to solve this question. If there are 120 calls, 13 agents answering calls, what is the probability or the odds of one agent getting the ...
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3answers
66 views

Intro to Probability

A person randomly places 9 rooks on a 9 by 9 grid (the 8 by 8 case corresponds to a chess board). What is the probability that none of the rooks can capture any of the other rooks? I have a good ...
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0answers
18 views

Quadratic variation question

Let $M$ be a vector of local martingales. Then there exist an increasing and adapted $C$ and optional processes $\sigma^{ij}, i,j=1,...,d$ such that $<M^i,M^j> = \int_0^. \sigma^{ij} dC_s$. Can ...
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1answer
27 views

Calculate probability of joint PDF

I'm given the following joint PDF and asked to calculate $P(X+Y>1)$ $f_X$$_Y$$(x,y)=2/5$ for $0<y<1$ & $0<x<5y$ and $f_X$$_Y$$(x,y)=$ $0$ else I know I have to take the ...
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votes
1answer
19 views

an urn contain four white and six black ball,another urn contain eight white and nine black balls.A [closed]

an urn contain four white and six black ball,another urn contain eight white and nine black balls.A ball is drawn from the first urn and put in the second and then a ball is drawn from the second.find ...
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2answers
25 views

Odds of failure over time.

I was having a discussion with a friend about a video game we're playing an how unlucky I've been with the odds of something occurring and I'm curious to see just how unlucky I've been. Please excuse ...
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0answers
21 views

Value of the game involving guessing the total of two dice [closed]

You pick a number between 2 and 12. Then you roll two dies. The result is the sum of the dies. If your number is not the sum of the dies you lose a dollar If your number is the sum of the dies you ...
3
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0answers
57 views

Using Jensen's inequality to prove the Cauchy distribution has no mean

I can see that there is no mean because $\int x / \pi(1+x^{2})$ does not converge from -inf to inf. But my prof hinted at using Jensen's inequality for the proof. $$f(E(X)) \le E(f(X))$$ How can I ...
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0answers
14 views

Psudorandom number from diffrent generators.

Suppose I've N random number generators (uniform distribution) and I take 1 value from each one. Will this set of N variables be considered equivalent to N random numbers produced by a single ...
3
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0answers
37 views
+100

Convergence in distribution of stochastic equation solutions

I'm studying from Kurtz's book "Markov Processes Characterization and convergence" and I have a question about the convergence of processes in $\mathbb{Z}^d$ that are solution of some equation. (see ...
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2answers
20 views

When does probability mass outside a sufficiently large ball is small?

Many times when I read books about statistics or probability theory, I encounter proofs which said: For any $\epsilon>0$ there is an $M\in(0,\infty)$ such that $\text{Pr}\{X\in ...
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votes
1answer
36 views

Birthday paradox derivation: different approach

I usually use randomization in algorithms so I am familiar with basics of probability but nothing much advanced. I have gone through the derivation for Birthday Paradox (Cormen et al) and decided to ...
0
votes
1answer
21 views

If the side length of a square follows uniform distribution, how to find the mean and variance of its area?

A square has side of length $X$ cm, where $X\sim U[4,10]$. Find the mean and variance of the area of the square. I understand how to get the mean and variance for the length of each side, but simply ...
0
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0answers
21 views

Find the probability of the event that number 5 and number 10 were chosen first and last, respectively at the experiment of choosing six numbers, if: [closed]

a) the choices are with replacement and order is not count; b) the choices are without replacement and order is not count; The set is : {1,2,3,4,5,6,7,8,9,10} I am quite new at this so any help ...
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0answers
34 views

Question on Probability, Please Help! [closed]

Two students take a test consisting of five true/false questions. To pass the test the students have to answer at least three questions correctly. Both of them know the correct answers to two ...
2
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1answer
66 views

Correlation of a vector generated and its one-period lag, both generated using AR(1) data

Suppose that $C_0$ is $100$ and $\{e_t\}_{t\geq 1}$ is a sequence of i.i.d. standard normal random variables. We generate $C_t=C_{t-1}+e_t$ for $t\geq 1$ and set $$ x_t=C_t^2-C^2_{t-1},\quad ...
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1answer
19 views

Basic set theory and probability

I need to prove the following but they all seem too obvious to need a proof. For the third one, for exmple, should I argue something along the line of $A\cup A^c=U$? Thanks in advance. $A=(A\cap ...
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2answers
27 views

Need clarification on Independent Events Probability question

In the World Series of baseball, two teams A and B play a sequence of games against each other, and the first team that wins a total of four games becomes the winner of the World Series. If the ...
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1answer
41 views

How to approach analyzing probability problems? (Specific question included)

I've recently become very interested by the concept of probability. After doing some studying, I believe I've become fairly familiar with the terms: probability, random variables, probability ...
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0answers
15 views

Kullback-Leiber divergence for two simple probability vectors

For any probability vectors $ p= (p_1,...,p_K) $ and $ q=(q_1,...,q_K) $ representing monotonically increasing functions $ x-1 $ and $ ln(x) $ respectively what is the KL divergence? $$ KL(p||q) = ...
0
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1answer
29 views

Probability density function of $max(X,Y)$

Assume we have random variable $W = \max({X,Y})$, I would like to find the pdf of $W$. This is what I have done. $$ F_W(w)= \mathbb{P}[ W\leq w]=\mathbb{P}[ \max({X,Y})\leq w]=\mathbb{P}[ X\leq ...
3
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2answers
354 views

Combinatoric Solution To The Birthday Paradox

I attempted the following solution to the birthday "paradox" problem. It is not correct, but I'd like to know where I went wrong. Where $P(N)$ is the probability of any two people in a group of $N$ ...
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1answer
25 views

Expected value of a series [closed]

Suppose you had a random series with a finite sum. What is the expected value of this sum?
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0answers
36 views

How to approach solving multi-variable continuous probability distrobution problem

You are taking the subway in an unfamiliar city. You are told to take the Blue Line train to central station and then transfer to the Green Line train, which is just on the other side of the platform. ...
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0answers
24 views

Random-walk in a pentacle (5 nodes)

There are a total of 5 nodes at the edge of a pentagram At each node, you have a 4 choices which will lead you to either a destination node or non-destination node. Assume the decision of path is ...
1
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0answers
33 views

Probability of sum of independent variables less than amount

I have an ungraded homework assignment that has had me stumped for the better part of an hour. I have a really ugly solution but honestly I'm just not sure where to start. This is what I have so far: ...
0
votes
1answer
62 views

Conditional expectation w.r.t. random variable and w.r.t. $\sigma$-algebra, equivalence

Let $\Omega = \{ \omega_i \}$ be a countable set, and consider some probability space $(\omega, \mathcal F, P)$ with $p_i := P(\{ w_i \})$. Let $X : \Omega \to \mathbb R$ be a random variable, then ...
0
votes
1answer
10 views

Convergence in distribution of a normalized Poisson distributed random variables

Show using the central limit theorem that $\frac{X_n-n}{n^{1/2}}\rightarrow Z$ where $Z$ is standard normally distributed and $X_n$ is $Poisson(n)$ distributed.
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1answer
41 views

Show martingale space is a Banach space

Let $\mathcal{H}^1 = \{M \in \mathcal{M}, E[sup_{t\geq 0} |M_t|] < \infty\}$, where $\mathcal{M}$ is the space of right continuous with left limits martingales. Show that $\mathcal{H}^1$ is ...
0
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1answer
26 views

Suppose $X$ and $Y$ are independent exponential random variables with the same mean $µ = 1/2$. Let ($Z,W) := (X,X +Y)$

Suppose $X$ and $Y$ are independent exponential random variables with the same mean $µ = 1/2$. Let ($Z,W) := (X,X +Y)$ i) Find the regions where the joint pdf of $(Z,W)$ is positive. ii) Find the ...
0
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0answers
15 views

The bound of Rayleigh quotient

Suppose $A$ and $B$ are some random positive definite matrix (e.g., covariance matrix) draw from some distribution. And I want to compute ...
1
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0answers
57 views

Probability - Hausdorff distance

On a 4x4 table 2 coins with radius 1 are thrown.They may overlap partially or completely but remain completely on the table.What is the probability that Hausdorff distance between the two nickels to ...
0
votes
1answer
23 views

An example of covergence to an exponential distribution, the role of continuity

I got a probability problem I can solve, but my solution does not use an assumption which is given in the formulation of the problem. I am afraid that this is might be a sign that my solution is ...
0
votes
2answers
33 views

Why would a uniform prior distribution give a different result than a purely frequentist approach?

I would expect a uniform prior to be a good example of an uninformed prior and get the same result as the frequentist approach. However, this is not the case. As an example, let's look the classical ...
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1answer
22 views

Showing independence of two random variables

The problem is here The trouble im having is showing how $\bar{x}-\bar{y}$ is independent of $S_{pool}$. I know the covariance of ( $\bar{x}-\bar{y}$,$X_i-\bar{x}$)=0 and similarly for the other ...