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A probability provides a quantitative description of the likely occurrence of a particular event.

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Construct Confidence Curve in R in Change Point analysis

I am trying to reproduce the journal article "Confidence distributions for change-points and regime shifts" (on page 16 top left hand corner) Firstly, I generated random sample using i) N(1,1) and ii)...
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2answers
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Calculate probability of pattern of indipendent events

I have a long list of independent events. Of these, $71\%$ are WINS and $29\%$ of them are LOSSES. I have calculated the probability of losses with this formula : \begin{align} 0.29^2 &= P(\text{...
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1answer
26 views

Does the occurrence of an event give any information on it's probability?

Say you know the outcome of an event. You don't know the probabilities of the event happening or not. Can you infer any information by the occurrence of that event happening? i.e. You have a deck of ...
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1answer
32 views

Is this method of finding the expected value of the square a random variable correct?

Suppose x is a discrete random variable with values 2,3,1 and probabilities 0.2,0.3, and 0.4 respectively. NOw say we have the function y=x2+3 and we want to find the expected value of this equation. ...
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2answers
136 views

Marginal distribution of normal random variable with a normal mean

I have a question about calculation of conditional density of two normal distributions. I have random variables $X|M \sim \text{N}(M,\sigma^2)$ and $M \sim \text{N}(\theta, s^2)$, with conditional ...
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0answers
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Survival probability of a random walk with renewal timings

A random walker starting at time $t=0$ and location $x=0$ moves to the right ($x+1$) or the left ($x-1$). The $k^{\mathrm{th}}$ moves to the right and left occure at the times $\sum_{i=1}^{k} R_i$ and ...
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33 views

$X$ and $Y$ are independent and have the same law then $(X,X+Y)$ and $(Y, X+Y)$ have the same law

My background is in maths so don't have "deep" knowledge or intuition about the topic. The argument that's presented says that can write $(X,Y)=(Y,X)$ so i can write $(X, X+ Y ) = (Y, Y + X ) = ( Y, X+...
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2answers
70 views

How to determine the number of possible combinations of letters that contain a degenerate substring

I've been racking my brain for a couple of days to work out a series or closed-form equation to the following problem: Specifically: given all strings of length $N$ that draws from an alphabet of $L$ ...
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2answers
490 views

Trouble understanding Bayes Theorem

I was watching a video on YouTube and i am not sure if the given solution is correct. Can someone confirm?
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1answer
43 views

Probability of passengers exiting an elevator

I'm not sure if I'm doing this problem correctly. The question is to ...
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1answer
21 views

With 48 bit (random) image data and 36 Megapixels / frame, how many shots for 50% chance of dup pixel? [on hold]

If you have 48 bit sensor data per pixel and 36 megapixels per frame, how many pictures would you have to take to have a better than even chance of finding a duplicate pixel value? Assuming that each ...
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1answer
24 views

Bridge Hand Probabilities

Each of the 4 players in the game of bridge get dealt 13 cards. One player and his partner can see they hold 8 of the heart cards so they know that the 2 remaining hands they can't see hold the ...
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22 views

Simple confusion on joint likelihood and MAP inference

In probability we have: $$ P(A, B \mid C) = P(A \mid B, C) \, P(B \mid C)$$ which makes sense. But (it is given in a lecture I am following that) we also have that MAP inference returns the ...
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0answers
13 views

What is the name of this test for the probability of differences between lists and is it valid?

And are there any better methods? In a 1969 book about investing, the author describes a method for assessing the effectiveness of a stock picker. Ask the picker to provide a list of n stocks that ...
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0answers
38 views

What is the difference between Likelihood, Conditional Likelihood and Conditional Probability? [duplicate]

As the title says, what is the difference between Likelihood, Conditional Likelihood and Conditional Probability? As simple an explanation as possible without losing any meaning (perhaps with an ...
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0answers
38 views

Ratio of mean absolute deviation to standard deviation under normal distribution

Can someone show why the ratio is $\sqrt{\frac{2}{\pi}}$ ?
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1answer
20 views

Law of total probability - Continuous conditioned on discrete?

Let $Y \sim f_Y (y)$ be a strictly continuous r.v. Let $S \sim p(s)$ be a strictly discrete r.v. Can you write the density $f_Y (y)$ as $$f_Y (y) = \sum_S f(y|S=s)p(s)$$ I know the law of total ...
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1answer
21 views

Probability of Equipment Failure

I have a set of 25 equipment. Each equipment fails (and recover) once a month, on average. a) What is the probability that 2 equipment will fail on the same day? What is this probability in terms of ...
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1answer
42 views

How to calculate the integral of Normal CDF and Normal PDF?

I'm trying to find $\int_{\frac{a-b}{B}}^\infty\Phi\left(tA+ABx\right)\phi(x)\,dx$ where $A = \frac{\sqrt{\gamma_{3}+\sigma_3^2}}{\gamma_{3}},\ B = \frac{\gamma_{2}}{\sqrt{\gamma_{2}+\sigma_{2}^...
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1answer
43 views

the meaning of likelihood in maximum likelihood estimation

To my understanding, likelihood has no meaning per se. Only by comparing likelihoods do they become intepretable. Likelihood is unbounded and probability is bounded. In maximum likelihood estimation,...
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1answer
59 views

Beta Distribution and how it is related to this question

Let $f(x) = k(\sin x)^5(1-\sin x)^7$ if $0 \lt x \lt \pi/2$ and $0$ otherwise. Find the value of $k$ that makes $f(x)$ a density function. I'm struggling to understand how this relates to the Beta ...
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Probability of never returning to the origin until time $2n$ in asymmetric Bernoulli random walk

I have the following asymmetric random walk problem. $X_1, \cdots, X_{2n} \overset{iid}{\sim} F(p)$, where $F(p) : \begin{cases} P(X = 1) = p \\ P(X = -1) = q=1-p\end{cases}$ So what I need to ...
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3answers
84 views

Conjugate prior, unclear definition

Consider the following definition: A family $\cal F$ of probability distributions on $\Theta$ is said to be conjugate (or closed under sampling) for a likelihood function $f(x|\theta)$ if for every $\...
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1answer
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Calculate advantage of Serves in Table Tennis

In table tennis there's an ongoing controversy about "illegal" serves. Often the question arises how strong the influence of serves on winning probability is. I stumbled upon a recent paper, but I ...
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28 views

calculate binomial deviance (binomial log-likelihood) in the test dataset

I'm predicting probabilities $P(Y=1)$ using a probability forest (ranger in R). I want to evaluate my predictions $\hat p_i$ in a test dataset by calculating average binomial deviance (log likelihood)....
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1answer
25 views

In a probability generating function, what exactly is the parameter of G(z)?

For instance, given $\DeclareMathOperator{\P}{\mathbb{P}} \DeclareMathOperator{\E}{\mathbb{E}} G(z) = \E z^X$, what exactly is $z$? and also what does the generating function actually give you? ...
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0answers
20 views

The “Birthday Problem” generalized to continuous time rather than days [duplicate]

In the original “Birthday Problem”, the year is divided into 365 discrete days, and a “collision” is defined as being born on the same calendar day. Using this definition, two people can be born two ...
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1answer
38 views

probability of repeated events

I have a website and I want to calculate the probability of clicks on the ads. Let the probability that each user clicks on a link be p (something like ...
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0answers
19 views

Probability calculation for posterior information [closed]

Assume there are 400 athletes in a training camp, who are required to attend the morning drill starting at 4 am. The attendance in morning drills is 70%, i.e. on an average, 280 athletes are present. ...
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2answers
55 views

Is there any truth to the phrase “statistics mean nothing to the individual”?

Some sources claim that IQ is correlated with academic and/or professional success. Let's assume there is a correlation of 0.5 between IQ and University GPA, discovered from a study of a very large ...
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1answer
14 views

Evaluating usefulness of estimations of a parameter for different distributions

If I had a sample of size n and wished to estimate some parameter, say p for two different distributions from the produced sample what would be required to determine which was more useful? Assume the ...
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0answers
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How to interpret the probability density function exceeding one over a finite interval? [duplicate]

If one looks up 'Frechet Distribution' on wikipedia, one will find the following figure in the top-right of the page I was under the impression that the integral of the PDF function taken from ...
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1answer
33 views

What percent of males in the sample own their own home?

I said it was (males who own a house) divided by total number of males: 132 / (132 + 50) which equals to 72.5% However, my professor seems to think it is the # of male who own the house divided by ...
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1answer
111 views

Maximum Likelihood Estimate for a likelihood defined by parts

Suppose $X_1$, . . . , $X_n$ are i.i.d random variables having pdf $$ f(x\mid\theta)= \begin{cases} \frac{4}{\theta}-\frac{4x}{\theta^2} & \frac{\theta}{2} \lt x \lt \theta \\ \frac{4x}{...
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1answer
31 views

Combining P-Values from multiple trials of the same experiment

this is my first question here, a little background about me, im a biomedical engineer, im studying a PhD in Neuroscience, and a Micromaster in Statistics and Data Science. Here in my lab, very few ...
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0answers
28 views

Generate Keys with diverse [closed]

I am working on program that on one of the step I need to generate a key(256)bits to encrypt something. The key has to be unique in specific way . The key has to be binary[1,0,1..], (256)bits long ,...
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29 views

Jensen–Shannon divergence relation between marginal and joint

I have the following distributions- Joints: $p_1$(x,y) = $\rho_1$(x) $q_1$(y|x), $p_2$(x,y) = $\rho_2$(x) $q_2$(y|x) And the marginals: $\rho_1$(x), $\rho_2$(x). Is it possible to provide any ...
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How do document lengths affect Gaussian Naive Bayes?

I'm trying to understand Gaussian Naive Bayes. I am training on a pre-processed subset of the 20 Newsgroup data. Each observation is around 500 attributes (words), and 1 class (of 5 possible). I ...
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0answers
32 views

Single Sample vs Population Non-normally distributed

I have rna-seq gene expression data (but could also be reads assigned to species) where most of the genes are expressed at low levels, and the units are discrete ranging from 0 to the total number of ...
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0answers
18 views

Inducing relative class frequency/ soft (voting) probabilities for classification Random Forests in R [duplicate]

(The following question concerns binary classification) As discussed in other posts, when using Random Forests for classification one maybe not just interested in the output class (i.e. 0 or 1) but ...
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0answers
14 views

Difference between discriminative and generative learning algorithms?

I know there is a lot of different posts about this, and I've read at least a couple of them, and I think to a very small extent I understand what it is about, we can either use a discriminative ...
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17 views

How to integrate probability density of sum of two indepedent random variables with a finite lower bound on one of them?

$$\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{-u^2/2}\:du=1$$ but $$u = \ln(A)-C-k$$ where $\ln(A)$ and $C$ are normally distributed independent random variables, and $k$ is a constant. I am ...
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2answers
30 views

Forecasting From an Age-based Distribution

I have an age-based probability distribution that looks something like this, where the age is in rows, and the year is in columns: ...
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1answer
3k views

How many times must I roll a die to confidently assess its fairness?

(Apologies in advance for use of lay language rather than statistical language.) If I want to measure the odds of rolling each side of a specific physical six-sided die to within about +/- 2% with a ...
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1answer
29 views

How can a dnorm probability be larger than a corresponding cumulated pnorm probability [duplicate]

Using the probability distribution density functions dbinom, dnorm, etc. and the corresponding cumulative probability functions pbinom and pnorm, I noticed that the dnorm density values could be ...
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1answer
22 views

A fair die is thrown two times independently . Let X,Y be the two outcomes of these two throws and Z= X+Y [closed]

U is the remainder obtained when Z is divided by 6. X and Z are independent ? X and U are independent ? Z and U are independent ? Y and Z are not independent ?
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2answers
90 views

Is it true that P(X|Y)=P(Z|Y) implies P(X) = P(Z)? [closed]

Something feels intuitively off about this but I can't find a way to algebraically manipulate it to be false. Thanks :)
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Sentiment analysis probabilities

I'm looking into a Kaggle dataset of news article with three columns for the results of sentiment analysis for news items, each about a different company. The columns present the results of ...
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1answer
18 views

Multiplying two event with probability density function, is it possible?

in my exercise, $X$ is the size of a tree trunk, and $X$ follows a normal distribution $\mathcal{N}(9,0.4)$, we want to know $P(8.8\le X\le11.2)$ So I though that I could do this: $P(8.8\le X \le11.2)...
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2answers
31 views

Intuitive explanation from regression coefficient estimate formula

Can someone provide an intuitive explanation of why the OLS regression estimate, of y=a+bx, b have the form b=cov(x,y)/V(x). How intuitively are the covariance and variance related in this?