Tagged Questions
A probability provides a quantitative description of the likely occurrence of a particular event.
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0answers
7 views
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)...
0
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2answers
21 views
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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votes
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. ...
3
votes
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 ...
1
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0answers
17 views
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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0answers
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 $L$ ...
2
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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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votes
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 ...
2
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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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0answers
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 ...
1
vote
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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votes
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}^...
2
votes
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,...
6
votes
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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0answers
23 views
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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votes
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 $\...
2
votes
1answer
17 views
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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0answers
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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votes
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? ...
1
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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 ...
1
vote
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 ...
-1
votes
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. ...
-1
votes
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 ...
2
votes
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
12 views
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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votes
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 ...
2
votes
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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votes
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 ...
1
vote
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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vote
0answers
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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votes
0answers
14 views
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 ...
1
vote
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 ...
0
votes
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 ...
0
votes
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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votes
0answers
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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vote
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:
...
21
votes
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 ...
0
votes
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 ...
0
votes
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 ?
2
votes
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 :)
1
vote
0answers
13 views
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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votes
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)...
2
votes
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?
