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
48 views

Introductory (online) texts on Bayesian Network.

I would like to ask for some recommendation of introductory online texts on Bayesian Network. What I am searching for is some accessible and instructive text not necessarily covering the subject in ...
4
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4answers
172 views

Mlodinow. The Drunkard's Walk. An example from the book.

This excerpt is from Leonard Mlodinow's book The Drunkard's Walk: And although Fortune is fair in potentialities, she is not fair in outcomes. That means that if each of 10 Hollywood ...
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2answers
56 views

combinatoric problem related to drug

i want to choose optimal decision from following problem Imagine having been bitten by an exotic, poisonous snake. Suppose the ER physician estimates that the probability you will die is $1/3$ unless ...
4
votes
2answers
116 views

Markov and independent random variables

This is a part of an exercise in Durrett's probability book. Consider the Markov chain on $\{1,2,\cdots,N\}$ with $p_{ij}=1/(i-1)$ when $j<i, p_{11}=1$ and $p_{ij}=0$ otherwise. Suppose that we ...
3
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2answers
113 views

Are $|X|$ and $\operatorname{sgn}(X)$ independent?

Let $X$ be a real valued random variable. Let $\operatorname{sgn}(x)$ be $1$ when $x>0$, $-1$ when $x<0$ and $0$ when $x=0$. Why are $|X|$ and $\operatorname{sgn}(X)$ independent, when the ...
3
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2answers
341 views

Probability that a set of 'N' random binary strings are all at least a certain Hamming distance 'k' apart

Imagine I have a set of $N$ binary strings of length $L$, where I generate each string randomly (say, by flipping a coin for each bit). What is the probability that all $N$ strings are at least a ...
0
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1answer
76 views

Sumset using first moment method

This is problem 1.1.6 from the book "Additive Combinatorics" by Tao and Vu. Suppose A is a subset of an additive group Z. We need to show that there exists a d-element subset of Z, denoted B = { v1, ...
3
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1answer
118 views

Completeness and separability of Lévy's metric

Let $D$ be the set of all functions $F: \mathbb{R} \rightarrow \mathbb{R}$ which are nondecreasing, left-hand-side continuous and $\lim_{x \rightarrow -\infty} F(x)=0$ and $\lim_{x \rightarrow ...
0
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1answer
64 views

Probability of a new number given a set of $n$ previous numbers?

I have a set of numbers (each one corresponding to a payment made from the same person) and I would like to assign a probability value to a new specified number given that historical data. I've ...
4
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0answers
129 views

Varieties and Statistics

Consider a random variable $X$ that can take on the values $0,1$ and $2$. So we have $$p_i = P(X=i), \ i = 0,1,2$$ $$\sum_{i=0}^{2} p_i = 1$$ and $$0 \leq p_i \leq 1$$ So identifying a random variable ...
0
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1answer
852 views

expected value for this question

A manufacturer buys an item for 1600 dollar and sells it for 2000 dollar. The probabilities for a demand of 0, 1, 2, 3, 4, “5 or more” items are 0.05, 0.15, 0.30, 0.25, 0.15, 0.10 respectively. How ...
2
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1answer
211 views

Is Fuzzy Logic Needed? [closed]

I had a very big doubt in my mind about Fuzzyness. When statistics is answering all the questions, which we see generally in Fuzzy theory. Then why one SHOULD learn Fuzzy Theory. Or is there any gap ...
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2answers
303 views

probability coin toss

I am working on some homework questions and I am done everything except this one last question which I am stuck at. I am uncertain of how I can explain or find the probability in this case. I had a ...
0
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2answers
177 views

Generating random numbers

Suppose I would like to generate random numbers in a way that they satisfy some probability distribution with a mean $\mu$ and standard deviation $\sigma$, what is a formula for that? Thank you.
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3answers
395 views

Probability of winning one of two tennis matches

The probability that George beats Larry in a tennis match is 0.75. If they play 2 tennis matches, what is the probability that George wins the first or second match but not both? I have no idea ...
0
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3answers
827 views

Probability of selecting 2 points on a straight line

On a straight line of length 10 cm, two points A, B are selected at random. What is the probability that $AB > 4$?
2
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1answer
72 views

Searching for a secret, given a non-uniform distribution

Let $s$ be an unknown bit string of length $n$. Let $p(i, b)$ be the probability that $i$-th bit of $s$ is equal to $b \in \{0,1\}$. What's the fastest method to find $s$, given the distribution ...
0
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1answer
72 views

concentration of random variables

Say we have the following inequality: $ A < B < C$ where $A, B$ and $C$ are positive integer-valued random variables. Assume that $A$ is concentrated in $O(m)$ values with high probability and ...
0
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1answer
2k views

How to find the joint probability distribution function from the marginal probability distribution functions

I have a variable x. I generate variables u=f1(x), v=f2(x), w=f3(x), z=f4(x). I have the marginal probability density functions of u,v,w,z. I wish to find the joint probability density function. The ...
1
vote
1answer
170 views

finding the distribution of two dimensional variable that is a function of two variables of a uniform distribution

I thought I understand the matter at hand but it seems I can't solve a basic exercise on the topic. I've got a random variable $(X,Y)$ that has a uniform distribution over $D = \left\{(x,y) : 0\leq ...
0
votes
1answer
399 views

Conditional Poisson process

I am having difficulty with the following problem: A store promises to give a small gift to every thirteenth customer to arrive. If the arrivals of customers form a Poisson process with rate ...
0
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1answer
112 views

What is the expected value of this simple random variable?

Let $X$ be some random variable. Now define a new random variable $Y$ such that it has a probability $p$ of taking some fixed number $a$, and a probability $(1-p)$ of being determined by $X$. What is ...
4
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2answers
97 views

Probability and game

This should be known as "gambler's ruin". In a game, at each step, you can win 1\$ or lose 1\$. Let $Z_i$ be a variable that can assume as values 1 or -1. Let $$ X_n=\sum_{i=0}^n Z_i . $$ Can you ...
0
votes
1answer
83 views

Why do v structures not contribute to flow of probabilistic influence?

I recently went through a video which said that in the relation x->W<-Y, X does not influence y.X has causal relationship to W and W has evidential relationship to Y .So will X not affect Y ?
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0answers
212 views

Monotonicity of expectation of a concave function of a random variable wrt the variance of the random variable

This is a question motivated from utility function. (See here and here.) I have been trying to develop some common sense in Economics by the way. Given a function $f: \mathbb{R} \to \mathbb{R}$ and a ...
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3answers
2k views

What is the probability of getting 2 people out of 10 with the same birthday?

If you have 10 people, what is the probability of 2 (or more) people having the same birthday?
0
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1answer
166 views

Show that the variance of this random variable is finite

Let $X$ be a random variable such that $P(X<-1)=0$. Assume also that $E[X]$ and $Var[X]$ are finite. Show that $Var[\log(1+\frac{1}{2}X)]$ is finite. I haven't been able to show this. Maybe this ...
4
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0answers
180 views

Probability that a random weight function on $K_n$ satisfies the triangle inequality

On a complete graph $K_n$, every edge is assigned a random real weight in $[0, 1]$. I am trying to calculate the probability that the weights satisfy the triangle inequality or even bounds on this ...
2
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3answers
2k views

Mutually exclusive events

Working my way through the following problem: Problem Suppose that $E$ and $F$ are mutually exclusive events of an experiment. Show that if independent trials of this experiment are ...
0
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2answers
1k views

Can the joint PDF of two random variables be computed from their marginal PDFs?

As the question says, is it possible to compute the joint PDF of two random variables using their marginal PDFs? For example, if we let $X$ and $Y$ be Gaussian random variables with known mean, ...
8
votes
6answers
542 views

Is $\frac{1}{\infty}$ equal zero?

After reading this paragraph: A simpler version of this distinction might be more palatable: flip a coin infinitely many times. The probability that you flip heads every time is zero, but it ...
3
votes
1answer
166 views

Dixon's random squares algorithm: a step in the proof of its subexp. running time

I am currently working to understand Dixon's running time proof of his subexp integer factorization algorithm (random squares). But unfortunately I can not follow him at a certain point in his work. ...
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1answer
74 views

A problem on joint distribution

Suppose that the joint distribution of $X$ and $Y$ is uniform over the region in the $xy$-plane bounded by $x=-1,x=1,y=x+1, \text{ and }y=x-1$. What is $\mathbb{P}(XY>0)$? What is the ...
2
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1answer
391 views

Understanding a Markov Chain

I am using a Markov Chain to get the 10 best search results from the union of 3 different search engines. The top 10 results are taken from each engine to form a set of 30 results. The chain starts ...
2
votes
1answer
63 views

naive bayes, understanding the correctness of a model and computation

I implemented naive bayes algorithm to predict an emotion ( happy , sad ) for blogs using the formula provided by Manning's Information Retrieval book http://nlp.stanford.edu/IR-book/pdf/13bayes.pdf ...
1
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1answer
236 views

Applying Dominated Convergence and/or Monotone Convergence for $|Z|^{1/n}$

Problem: I am self-learning about DCT and MCT and related Lemma's. I understand the theorems as constructed, but I am struggling to apply them. As an example: $X_n=|Z|^{1/n}$ where $Z\sim N(0,1)$ ...
1
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1answer
254 views

the probability of picking certain amount of items from a sack.

I need a help on calculating the probability. Here is the task that I can "translate" it into a probability task. Let's assume we have a sack with 12 items. There are 1 X item and 2 Y items and other ...
0
votes
1answer
225 views

Upper-tail inequality for t-distribution

I am interested in upper tail bounds (or bounds on deviation from the mean) for t-distribution with n degrees of freedom (http://en.wikipedia.org/wiki/Student's_t-distribution) A bound that is of the ...
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2answers
105 views

Covariance 's relationship with pure math and probabilty? [closed]

I've been looking up a lot of statistical books and cannot find out mathmatical insight behind it, but my math level wasn't allow me to read the mathmatical statistics books and get the math behind ...
2
votes
2answers
378 views

Tennis Probability

Player A wins 90% of matches Player B wins 60% of matches If they play each other what is the probability that; Player A will win Player B will win
2
votes
1answer
143 views

Probability of sequence being longer than some length

We are given random bit generator which generates 0s and 1s with equal probability 1/2. We have an algorithm which generates random numbers using this random bit generator in this way: we look for ...
0
votes
1answer
313 views

convergence in probability and mean square

If we have a sequence of independent random variables defined as: Y$_n$= $a$+$n$ with probability 1$/n$; and Y$_n$=$a$ with probability 1-1$/n$; 1-Is the sequence converges in probability? 2-Is the ...
2
votes
1answer
101 views

Random variable and expectation

This is a part of an exercise that I'm doing, in Durrett's Probability book. Let $X$ be a r.v which is not constant. Let $\phi(\theta)=E\exp(\theta X)<\infty$ for $\theta\in(-\delta,\delta),$ ...
1
vote
1answer
229 views

Expectation of a minimum

Why is this: $E(\tau \wedge T) = \int_0^Ttf_\tau(t)dt+T(1-P(\tau\leq T))$, where $f_\tau(t)$ is the pdf of $\tau$. I am thinking its because $E(\tau \wedge T) = \tau P(\tau\leq T)+T(1-P(\tau\leq T))$ ...
0
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0answers
53 views

Inflation of Odds Ratios

Ioannidis 2005 states that, for a study with two groups (one control, one experiment), N = 2000, and true odds ratio of 1.1, the median observed odds ratio will be 1.23 among studies reaching ...
2
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0answers
110 views

Simulating first passage times

I have a Brownian motion $X_t = \mu t+\sigma W_t$, where $W_t$ standard Brownian motion. I know that the first passage time $\tau = \min\{t|X_t\leq\alpha\}$, is Inverse Gaussian distributed i.e., ...
1
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1answer
67 views

Two sequences of random variables

Consider two sequences of random variables $X_n, Y_n$ and suppose $X_n\to X$ in distribution. Does the following hold: $\lim_{n\to\infty} E[|X_n-Y_n|]=0 \implies Y_n\to X$ in distribution?
3
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3answers
276 views

arbitrary three points on a circle

Three points $A,B,C$ are chosen randomly on a circle.Find the probability that $\angle ABC$ is less than $\theta \in (0,\pi)$. My method of solving this problem is this: Fix a point $B$ on the ...
1
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2answers
184 views

What is the best choice in a win/lose game and how to calculate it

Say you have an amount of 350 creditsand you have 4 options: 1) put 50 credits and in case of a win you double your credits to 100 and therefor you have total a of ...
0
votes
1answer
213 views

game show problem [duplicate]

Possible Duplicate: The Monty Hall problem You are in a game show. You have to choose between three buttons, A, B and C. Pressing one of them will give you £200,000, and pressing either of ...