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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1answer
15 views

Birthday problem with duplicate days of the month

"Consider the birthday problem except that you ask for duplicate days of the month (assume each month has exactly 30 days)." The answer I got as well as the one given in the book is 7. After 7 ...
1
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1answer
39 views

Difficult arithmetic trying to follow textbook in probability

Struggling with some steps from my textbook: This is what i have been given: $s(1)=0$ , s(0)=1 and $s(s(x))=x$ (in other words a self-reciprocal function) $$x s\left(\frac{s(y)}{x}\right)=y ...
0
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2answers
33 views

How does probabilities cope with determinist systems?

Foreword, I have a stronger background in philosophy than mathematics, but I am interested in linking the two topics. So I excuse in advance if this question feel silly; Also please delete/close it if ...
1
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1answer
32 views

Having the highest value in a interval appear less often

I have an array of size 5. And initially in each index, they are initialized with the value 1. so it looks like this : 1 1 1 1 1 Every iteration, I get a decimal value between 0.0 and 1.0. At the ...
0
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0answers
33 views

Zero conditional entropy

This question is related to this math.se question but I need a bit more guidance. For two discrete random variables $X,Y$ we define their conditional entropy to be $$H(X|Y) = -\sum_{y \in Y} Pr[Y = ...
2
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1answer
27 views

# of people that go to a clinic follows a poisson distribution of 4 per day…

I just had an exam and I wanted to discuss a specific question on it. I will do my best to recall the question. Suppose the number of people that go to a clinic follows a poisson distribution of 4 ...
0
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1answer
36 views

Show that if $\{X_n\}$ is a Markov Chain

Show that, if $\{X_n\}$ is a Markov Chain then $$P(X_n=j\mid X_k=l,X_m=i)=P(X_n=j\mid X_m=i),0\leq k<m<n$$ What I did is $$P(X_n=j\mid ...
2
votes
2answers
44 views

expected values of identically distributed random variables

Let $X$ and $Y$ be identically distributed random variables on some probability space $(\Omega,\mathcal{F},\mathbb{P})$. Then, if I let $F_X$ and $F_Y$ denote the distribution functions of $X$ and ...
0
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0answers
37 views

Does any one have a link to Jorm Steuding's Probablistic Number Theory? [closed]

I was reading it through the browser and the link on CiteSeer died. :( I will download it this time. Thanks. Regards, -EM
0
votes
1answer
39 views

covariance matrix of X+Y and X-Y

This question comes up in almost every past paper i do and is worth 10 marks and just can't work it out... Let $X$ and $Y$ have the joint pdf $$f(x,y)= \begin{cases} e^{-y}, \text{if} \ 0 < x ...
2
votes
1answer
41 views

Cumulative distribution function implication

How can I prove the following: Let $X$ and $Y$ be two random variables. Suppose that their cumulative distribution functions satisfies $F_X(x)=F_Y(x)$ for all $x$. How can I show that $X$ and $Y$ are ...
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2answers
39 views

Probability to remain at top surface of rubik's cube [closed]

There is an insect at the central square of the top surface of a rubik's cube. Every second the insect moves one block and it has to move every second. It can move only in forward, backward, left, and ...
1
vote
1answer
21 views

Expectation of exponential of integral of absolute value of Brownian motion

Sorry about all the "of"s in the title... here's my problem: I want to compute the expected value of $$ \exp\bigg\{ C \int_0^t |W_s|ds\bigg\} $$ where $W$ is a Brownian motion and $C$ is a positive ...
2
votes
2answers
50 views

Which one of the following versions of Bayes' theorem is correct?

I've seen two versions of Bayes' theorem: I've seen this very long version from a frequentist probability class: $$ P(B|A)=\frac{P(A|B)P(B)}{P(A|B)P(B) + P(A|B^c)P(B^c)} $$ where $B^c$ is the event ...
2
votes
3answers
52 views

Expected value of die rolls - roll $n$, keep $1$

I know how to calculate expected value for a single roll, and I read several other answers about expected value with rerolls, but how does the calculation change if you can make your reroll before ...
0
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0answers
18 views

Proving a combinatorics identity (permutations and combinations) [duplicate]

Prove the following identity by interpreting their meaning combinatorially. $$\left( \begin{array}{c} n \\ r \\ \end{array} \right)=\left( \begin{array}{c} n-1 \\ r-1 \\ ...
1
vote
1answer
45 views

Am I calculating probability correctly?

Probability was never included in my high school classes, so I'm trying to learn it now from the internet. The downside of this is that you don't get anyone grading your work and catching flaws. This ...
1
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3answers
43 views

Finding the probability of whether it would rain on weekends

The probability that it will rain on Saturday is 25% and the probability that it will rain on Sunday is also 25%. Is it true that the probability that it will rain on the weekends is 50%. Explain why ...
0
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0answers
21 views

inequality involving expectation of the maximum

For $X_i \sim$ i.i.d with cdf $F_x$, and $\forall c \in \mathbb R$, then, letting $M_n$ denote the maximum observation $$ M_n \le c+ \sum_i^n (X_i - c) \mathbb I(X_i > c) $$ I proved this by ...
0
votes
1answer
46 views

Birthday problem extension question

I have N balls and M boxes. The balls are thrown at random onto the boxes. What is the probability that some box contains at least 3 balls? Based on the Birthday problem, I know how to find the ...
0
votes
1answer
51 views

Question regarding Application of Combinations and Permutations (HW Problem)

I have a midterm I am studying for and I don't have the solutions to this homework problem. Can anyone please explain how to do it? I would really appreciate it. Here is the problem: I googled the ...
1
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0answers
32 views

Joint probability for discrete and dependent variables

Given $\bar{X} \sim N(\bar{\mu}, \sigma)$ is a vector of independent continuous random variables (with identical variance) and $Y_j = ( \bar w_{j} \cdot \bar X + b_j > 0)$ is a set of dependent ...
-2
votes
1answer
40 views

Suppose your mail gets moldy with probability q when sitting in the mailbox independently of whether mail is actually received in your mailbox [closed]

Suppose on any given day you receive mail in your mailbox with common probability p. Assume that whether mail is put in the mailbox or not is independent from day to day. Suppose your mail gets moldy ...
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0answers
43 views

Suppose I flip a coin that lands heads with probability 10 times. Find the maximum likelihood estimator [closed]

Suppose I flip a coin that lands heads with probability $\theta$, $ 10$ times. Let $Y_i$ be $1$ or $0$ depending on whether the i'th coin lands heads. Find the maximum likelihood estimator of ...
1
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1answer
35 views

Given a probability over time, predict when an event will happen

First of all, I'm asking this because I'm writing a game, so this is probably not a typical question in probability. However I'm new to game design so I don't even know what this would be called. ...
0
votes
2answers
42 views

Unbiased estimator of $\theta(1-\theta)$:Bernoulli Distribution

Suppose $X_1, X_2, \ldots, X_n$ are a Bernoulli($\theta$) with pmf: $$P(X|\theta)=\theta^X(1-\theta)^{1-X}, \; X \in \{0,1\}$$ Prove or disprove that $\bar{X}(1-\bar{X})$ is an unbiased estimator of ...
1
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0answers
28 views

Almost surely diverging sum implies almost surely diverging sum of conditional expectations?

Suppose $\sum_{n=1}^\infty X_n = \infty$ almost surely for nonnegative $X_n$. Let $\mathcal F_n = \sigma(\{X_0, X_1, \ldots, X_n \})$. Can we show that $\sum_{n=1}^\infty \mathbf{E} (X_n | \mathcal ...
-1
votes
1answer
21 views

Conditional independence expansion

I have four random variables A,B,C and S. A,B and C are conditionally independent given S. So, I need to obtain P(A,B,C,S) By the chain rule: $$P(A,B,C,S)=P(S)P(A|S)P(B|A,S)P(C|A,B,S)$$ By the ...
2
votes
0answers
30 views

The concept of correlation in functional analysis

I am currently reading a book "measure, integral and probability" by Capinski and Kopp. The correlation between random variables $X$ and $Y$ is defined as the cosine of the angle between $X_c$ and ...
1
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0answers
34 views

Probability Question [duplicate]

how would I be able to answer this question? The first box contains 3 white and 7 black balls, and the second box contains 6 white and 3 black balls, A ball is chosen at random from the first box, ...
1
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3answers
125 views

Why do we subtract [Combinatorics]

I asked Here This question and I am still confused. I got that, for at least one group together there are: $$3 \cdot 9 \cdot \binom{6}{3, 3}$$ But why do we subtract: $3 \cdot 9 \cdot 4$. Lets ...
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votes
1answer
34 views

can someone help me to answer this? [Mathematical expectation] [closed]

An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are $\dfrac1{12},\dfrac 1{12},\dfrac 14,\dfrac 14,\dfrac 16$ and $\dfrac16$, ...
0
votes
0answers
17 views

limiting and monotonic decreasing double sequence of probability measures

I am trying to figure out the behavior of this double sequence of measures. If I have a probability measure $\mu_n$ which is indexed by $n$, and a set of intervals $\mathcal{I}_k$ indexed by $k$ with ...
1
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0answers
34 views

probabilities of arrival time

John and Mary arrive under the clock tower independently. Let X be John's arrival time and let Y be Mary's arrival time. If John arrives first and Mary is not there then he will leave. If Mary arrives ...
1
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1answer
20 views

limit of CDF involving right extreme

I am trying to prove that if F is a cdf with finite right extreme ($\tau < \infty $), then $G=F(\tau - 1/x) , x>0$ is a cdf on $(0,\infty)$. For one of the steps: $$ \lim_{x \to 0} F( \tau - ...
5
votes
0answers
64 views

Bingo probability of a tie with 20 players

Assume "standard" bingo (75 numbers) with the columns ranging the following inclusive "semi-random" values B: 1 to 15, I: 16 to 30, N: 31 to 45, G: 46 to 60, O: 61 to 75. By semi-random I mean ...
-1
votes
0answers
19 views

probability measure conditional on a union of disjoint sets

I came across this in a proof in my text book but i can't quite comprehend. let $\mathbb{P}$ be a probability measure, $C$ and $D$ be disjoint non-empty sets. It is said that if we have ...
-1
votes
0answers
39 views

Independence and imaginary events

Consider this experiment: A 6-sided fair die is rolled. If it is a $1$, a fair coin is tossed. Otherwise, a 4-sided fair die is rolled. Assuming results of all die rolls and coin tosses are ...
0
votes
1answer
18 views

Probability measure on the space of $n \times n$ symmetric matrices with non negative integer coefficients

I know that there exists a particular measure, called Haar measure, defined on random matrices, i.e. $n \times n$ orthogonal complex matrices. My question is the following: can we define a ...
1
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1answer
35 views

Independence of random variables

Let $\{X_n\}$ be a sequence of independent random variables on some probability space. Then, by definition(according to the book that I am reading), I know that $\{\sigma(X_1),\sigma(X_2),\dots, \}$ ...
1
vote
1answer
28 views

Let $X$ denote the number of tosses required to get the 5th head and $Y$ the number between the 6th and 7th heads. Are $X$ and $Y$ independent?

Let $X$ denote the number of tosses required to get the 5th head and $Y$ the number between the 6th and 7th heads. Are $X$ and $Y$ independent? Y will always depend on X . NO ? i know geometric ...
0
votes
1answer
18 views

X denotes government will increase payment. x~Bin(2,2/3) . if one increment =9%. expected increment =?

If Government increases payment then they increase it by 9% . now if whether government will increase payment follows binomial distribution with parameters n=2 and p=(2/3) , then what percentage of ...
-2
votes
1answer
32 views

Regarding random variables [closed]

Let $X$ be a non-negative random variable. Prove that $$\Pr(X\geq a) \leq \frac{E[e^X]}{e^a}$$ where e is Napier's base. Can I know what the question means and how to prove it.
1
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3answers
57 views

Probability of finding item in a box

I'm trying to find if my approach to this kind of problems is correct. For example: You have 3 boxes, and you have a 33% chance of finding an item in a box. What is the probability of finding items ...
2
votes
2answers
148 views

2011 AIME Problem 12, probability round table

Nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one delegate ...
0
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0answers
21 views

How to determine the probability of seeing a time based event?

I am trying to figure out what the probability of capturing a time based event is. This is the situation. I'm observing a video of clusters of proteins in a cell with proteins tagged green and red ...
1
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2answers
53 views

Poisson Process Question - arrival times

Car crashes at a traffic stop arrive follows a Poisson Process with rate lambda = 2/hr. (a) Expected amount of time until the 2nd car crash arrives (b) P(See at most 2 car crashes during rush hour) ...
2
votes
1answer
38 views

how that $P(G)=1$ iff $\sum_n \Bbb P(A \cap E_n )=\infty$ for all events $A$ having $\Bbb P(A)>0$.

Two probability problems: 1. Let $a>0$ and let $X_n$, $n \geq 1$, be iid r.v. that are uniform on $(0,a)$ and let $Y_n = \prod_{k=1}^{n} X_k$. Determine all values of $a$ for which $\lim_{n ...
2
votes
1answer
19 views

Adapted random variable

Let $\{Y_n\}_{n=1}^{\infty}$ be a sequence of random variables, and let $F_n = \sigma(Y_1,Y_2,\dots,Y_n)$ for each $n$. Let $\{X_n\}_{n=1}^{\infty}$ be a sequence of random variables adapted with ...
1
vote
1answer
43 views

Question about Poisson process and arrival times

Problem: On any given day you receive mail in mailbox with probability $p$. Assume whether mail is put in the mailbox or not is independent each day. If the neighbor receive mail in his mailbox ...