# Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

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18 views

### Bayes' theorem and card colors

This is an expansion/generalization of a previous question I've asked here. Some of the simplifications I made in the original question turned out to be too simplifying, so I'm trying again. The most ...
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### Probability of getting a correct Bit

I have a probability problem that goes like this: I want to sent a bit across a channel that has a certain error rate. The probability of getting a bit wrong is $0.3$, and so to increase the chances ...
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### Martingales and stopping rules [closed]

\textbf{Question:} Let (X_1, X_2, \ldots, X_n) be a sequence of independent and identically distributed (iid) uniform variables on the interval ([-2, 2]), and define (S_n = X_1 + X_2 + \ldots + X_n). ...
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### Find marginal distribution of X and Y and the expectation of XY

This is an exercise that confuse me $$let \ \ x,y \in \{0,1,2......\}$$ $$\mathbb{P}(X=x,Y=y)=\frac{e^{-2}}{x!(y-x)!},x=\{0,1,...\}, y=\{x,x+1,...\}$$ $$otherwise \ \mathbb{P}(X=x,Y=y) = 0$$ In the ...
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### Given bivariate bernoulli with an integral as a parameter prove that are marginally identically distributed and correlation is positive

So this is a question from a past exam. The joint density function is \begin{aligned} P\left(X_1=x_1, X_2=x_2\right) & =I_{\{0,1\}}\left(x_1\right) I_{\{0,1\}}\left(x_2\right) \...
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### Picking random point many times on segment

Let $AB$ be a segment of length $1$. Let $P_1$ be a randomly chosen point on $AB$. Let $P_2$ be a randomly chosen point on $AP_1$. Let $P_3$ be a randomly chosen point on $AP_2$. ... Let $P_{10}$ be a ...
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### How to detect if a moving point has passed through the connecting line between two other fixed points?

I have a moving point (Tag) and two fixed points (anchors). I have the distance from the anchors to tag at each time. I also have the position of the anchors and the last position of the tag. I ...
1 vote
46 views

### Central limit theorem for inhomogeneous Poisson process

I consider $N_t$ an inhomogeneous Poisson process, especially $N_t$ follows a Poisson law with parameter $\int_{0}^{t}\lambda(s)ds$. We assume that $\frac{1}{t}\int_{0}^{t}\lambda(s)ds\to \sigma^{2}$ ...
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### How do I solve the average number of attempts to succeed when the probability increases with each failure?

Our base probability of success begins at .03 and each failed attempt increases the probability by .002 so that the second attempt has a probability of .032, the third .034, and so on. (The trials ...
58 views

### Recursive Expectation Question

Suppose we draw some k ~ Unif(0, 1). Then, we will draw some $u_1$ ~ Unif(0, 1). If $u_1 < k,$ we stop. Else, we will draw $u_2$ ~ Unif(0, $u_1$). We will continue drawing until $u_n < k.$ What ...
25 views

### What is the difference in my reasoning for sampling with replacement and the correct reasoning?

I am currently reading Blitzen and Hwang's Introduction to Probability book, and am on Theorem 1.4.7, which states that when you are sampling n objects and making k choices from them one at a time ...
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### probability distribution of total number of cells with 1/2 probability of dividing.

There is a cell that has a 1/2 probability of dividing into two daughter cells (the parent cell disappears) and a 1/2 probability of stop dividing. And each daughter cell has a 1/2 probability of ...
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1 vote
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### Probability question (standard - 12)

A matrix is choosen randomly form the set of matrix of order 3 elements of matries are 0, 1, 2 or 3. It is found that the matrix is diagonal matrix. Find the prob- ability that the matrix is non-...
39 views

### Brownian motion and logarithm inside averaging

We consider Brownian motion as a process $$V(0)=0, \qquad \overline{V(x)}=0, \qquad \overline{(V(x)-V(y))^2}= 2 |x-y|.$$ I do not know how to prove the statement:  \overline{\log\left(\int \mathrm{...
31 views

### The smallest d which almost ensures every polygon will contain expected number of samples +- d

Let's uniformly sample $n$ times from the unit square. Given $m$ polygons contained within the unit square with areas $A_i$, where $m = kn$, and where the polygons overlap arbitrarily, what is the ...
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