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Questions tagged [probability]

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

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How to find CDF of a function of continuous joint distribution from PDF of joint distribution?

Here's what I think I should proceed: Make a level curve for the function keeping the constraints given in the PDF of joint distribution in mind. Find the area of interest keeping the constraints ...
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Favorite sequence in 10 flip tosses

I have the following question. Somebody likes to flip coins. In particular, this person is delighted to get a sequence HTTH. Assuming the person flipped coins 10 times, what is the probability that ...
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Intuition behind product distribution pdf

Say we have two distributions $X$ and $Y$. I know that the pdf of the distribution $Z = X + Y$ is given by: $f_Z(z) = \int_{-\infty}^{\infty}f_X(x)f_Y(z-x)dx$ The intuition is that you sum up the ...
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cannot prove simple conditional probability

Is the next true? If so, why? P(A∩B|C) = P(A|B∩C) x P(B|C) I saw as part of solution of an exercise, but I can't prove that is true, how is it possible to arrive to that?
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Level curves and functions of pair of Random Variables?

I came across the following question: I tried solving it, the following is my 1st attempt:(2nd method at the end) 𝑃[𝑊≤𝑤]=𝑃[𝑋𝑌≤𝑤]=𝑃[𝑌≤𝑤/𝑋] And then I simply double integrated keeping the ...
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Probability of normal random variable yielding highest value among other normal variables

Let's say I have a competition with $N$ participants. Each participant yields a score that is normality distributed with unique means and unique variations. Each participant gets to post one score (we ...
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Expectation Maximization for a 2D Normal Model

I'm working through an example in Richard Duda's Pattern Classification on Expecation Maximization Algorithm. Specifically I'm trying to understand the expectation part, and how the parameters get ...
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How do I reconcile the output of a decision tree visual vs the output of the DecisionTreeClassifier class?

I have a decision tree model stored in dt. I also plotted and can visually see the decision tree itself. Given a new, unseen customer, I can use the visual tree to ...
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Calculate probability based on part of features

I have a knowledge base, where each row represent a class and columns represent features of classes: ...
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1answer
43 views

Why do we take a function of x as the limit of integration over y while calculating the marginal pdf of x?

I searched through similar questions but couldn't find one answering my question. I know the following is the way of finding marginal pdf from joint pdf. $$ f_x(x)= \int_{-\infty}^{\infty} f_{x,y}(x,y)...
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I have 3 gene datasets, 2 genes are sig in all 3, what is the probability of this being by chance?

I have three large RNA-seq datasets, two genes were found to be significant in all three datasets, what is the probability of this happening by chance? not sure what info i would need so here is ...
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Why is the relationship between max(X,Y) and X and Y the way it is?

My textbook says that the above follows from the observation: $\{W\leq w\}=\{X\leq w\},\{Y\leq w\}$, How do we prove the above observation?
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Football Pool Chances

I am trying to confirm the probability of being a weekly winner in an NFL football pool at least once during a given NFL season. The pool is set up as the following: Each player picks five teams ...
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1answer
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number of option to choose 5 couples of men and women [on hold]

I need help with the following question: There is 10 mans and 12 womens, how many options there is to make 5 couple (women,men)? I tought maybe (10 choose 5) - mens and (12 choose 5) women and 5! ...
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Probability of having a match in an existing database

Imagine you are an airport authority in CountryLand and you have two passenger types: human passengers and animals. There is no way for you to distinguish between human passengers and animals except ...
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Using binomial approximation to calculate probability

Question is as follows: In a shipment of $20$ engines, history shows that the probability of any one engine proving unsatisfactory is $0.1$. a) Use the Binomial approximation to calculate the ...
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Emergence of Lognormal distribution for the concentration of chemical compounds

I'm currently reviewing the literature about lognormal distributions describing/approximating the variability of a given chemical compound across different cells/ samples etc etc. The main argument ...
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Interpretation of Naive Bayes Probabilities

I'm dealing with a Naive Bayes approach to a Multiclass Classification problem with 9 different classes in the target variable. Let's assume the following: I've fitted a model to my training data and ...
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Joint probability distribution of some Gumbel differences

I would like your help to double check my derivations below involving the joint probability distribution of some Gumbel differences. Consider $K$ i.i.d. random variables $\epsilon_1,...,\epsilon_K$, ...
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1answer
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proof of independence of X-Y and X+Y when X,Y come from bivariate normal

I have a bivariate normal distribution: $$\begin{pmatrix} X\\Y\end{pmatrix} \sim \mathcal{N}(\mu, \Sigma)$$ where: $$\mu = \begin{pmatrix}\mu_X \\ \mu_Y\end{pmatrix}$$ $$\Sigma = \begin{bmatrix} \...
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Alternative to Hoeffding Bound in Streaming for Normally Distributed Variable?

I am reading a paper (Hellinger Distance Trees for Imbalanced Streams by R. J. Lyon, J. M. Brooke, J. D. Knowles, B. W. Stappers) on using the Hellinger Distance for Very Fast Decision Tree (VFDT)...
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How to simulate, if a customer will buy

If customer 1 will buy a product with a probability of 0.6 and every following customer 0.7, how can I simulate a system with n customers? The result should show which customers bought and which ...
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How to figure out whether a coin is “weighted” with some number of flips

Suppose there's a weighted coin. That coin either lands on heads every 1/10 times it is tossed, or it never lands on heads at all. I don't know whether that coin is the type of coin that lands on ...
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How to calculate coverage probability in R for cauchy distribution?

I know that the coverage probability is $P(|\hat{\theta}-\theta|\leq\epsilon)$. My task is to compare estimators of the Cauchy distribution for the location $\theta$. I've plotted the estimators and ...
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Addition of Gaussian with Gaussian [duplicate]

Hi I have following equations, where $T_1$,$T_2$ and $T_3$ are distributed as Gaussian.I want to know their mean and Variance. finally, I want to add them. How can I do that? All variables are ...
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Probability of a positive outcome from 2 events that have a 2% chance of a positive outcome

Apologies for my lack of maths jargon and terminology. This seems like a very simple problem to solve. I need a formula to determine the following; If event A has a 2% chance of success If ...
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1answer
41 views

How to estimate the mean and variance of a Gaussian distribution variable? [on hold]

I have two variables 2X and 0.5Y, both are independent and follows Gaussian distribution. How to estimate their mean and variance analytically? I want to know their individual mean and variance, then ...
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How is $s^k$ in p.g.f. likened to Dirac measure $\delta_k$?

How is $s^k$ (sometimes $z^k$, $\theta^k$) in probability generating function likened to Dirac measure $\delta_k$? I don't see how these are similar. Yet I see them equated. Clearly the Dirac ...
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1answer
23 views

Is this a t-distribution problem?

The problem says that the probability of student failure is 0.4 A random sample of size 10 is taken from this population. I'm asked to find the probability that, at most, 30 % of students failed. I ...
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Markov chain questions [closed]

please answer 2, 3, 4, 5, 6, 7 please answer no. 2, 3, 4, 5, 6, 7 questions
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1answer
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PDF of the minimum of a geometric random variable and a constant

I have $X \sim Geo(p)$, such that $$p(x) = (1-p)^{k-1}p, \ \ x = 1,2,3, \ldots$$ and Y is a constant random variable which assumes the value of the constant integer $t$, such that $$P(Y=t) = 1, \ \ ...
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Predicting whether a potential business agreements will be won or lost [on hold]

I am currently working on a project using a sales system and trying to come up with a way to use the current pipeline of potential sales to predict if the business agreements will win or lost based on ...
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1answer
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Summation of two Gaussian distributed data with different coefficient of mean and variance

I need some help on Gaussian distribution. i have two dataset, both are identical and independent distributed, but having mean as 2μ_1 and μ_2, same scenario for the variance. How can I add them? ...
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Probability density function units of the log-normal distribution

In a discussion on this forum lognormal distribution, standard-deviation and (physical) units the cumulative distribution function (PDF) of the lognormal distribution was analysed. The conclusion ...
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probability involves bivariate gaussian

I'm working on a spatial project. I need to calculate the probability of a point being the closest to another. Say I'm given four points $y$, $x_1$,$x_2$ and $x_3$ in 2D plane, and let $Y'=y+Z$, where ...
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Why is the Bayes predictor of the $0-1$ loss the maximum a posteriori?

Let $(X,Y) \in \Bbb X \times \Bbb Y$ be jointly distributed according to distribution $P$. Let $h: \Bbb X \rightarrow \tilde {\Bbb Y}$, where $\tilde {\Bbb Y}$ is a predicted output. $ $Let $L(h,...
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variance of a probability distribution [closed]

Can the variance of a Probability Distribution vary? For example, can there be a distribution on X such that when X>=0 variance is v1 and when X<=0 variance is v2?What are some example ...
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estimating the mean of constant + noise

(This is almost certainly covered in Statistics 101, but I missed that class..) I have a real-world sampled signal $S[t]$ that is a constant $\hat{S}$ plus some noise $\epsilon[t]$. My goal is to ...
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Probability to be present in every subgroup

Assuming you randomly split a set of n elements in $y$ equally sized parts(each has $x$ elements). Now you have a subset of m elements in the set of n elements ($m> (y/2)$). What is the probability ...
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1answer
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Finding the probability for non defective battery

A car manufacturer purchases car batteries from two different suppliers A and B. Suppose supplier A provides 60% of the batteries and supplier B provides the rest. If 6% of all batteries from supplier ...
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Calculate 5th percentile of a rate difference curve generated from a joint probability mass function

I have these curves below: These curves were generated using a library called discreteRV. ...
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Help Identifying the Name of a Theorem

Recall the following theorem: Let $X$ be a random variable with probability density function $f_x(x)$ and let $g$ be monotone over the support of $f_x$. The random variable $Y=g(X)$ has density $$...
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What is the probability that two samples from a source have no overlap?

I picked 29 results from a list of 429 results. I then picked a second group of 27 (with replacement) results from the same list of 429. There was no overlap between the two samples. What is the ...
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1answer
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Distribution of Maximum Likelihood Estimator

Why is the Maximum Likelihood Estimator Normally distributed? I can't figure out why it is true for large n in general. My attempt (for single parameter) Let $L(\theta)$ be the maximum likelihood ...
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Clarification on the concept of “General formulation of the problem of statistical inference” - Wald

I'm looking for clarification on one part of this definition, but also some feedback on my interpretation of the whole concept. The definition comes from the end of the first chapter of On the ...
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1answer
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Does number of people participating in a draw affect one's chances?

I have question that I haven't been able to find an answer to. Assume a scenario where there are two raffle events. There are 25 tickets in one and 100 in the other. Also assume that, in both events ...
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1answer
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From normal dist. with unknown variance, how to compute $P(\bar X>c)$?

We have $X_i \sim ^{iid} N(\mu,\sigma^2)$with known mean $\mu$, and unknown $\sigma^2$. Let's suppose we're given $s^2$ (sample variance) and $n$ (sample size). We know $\frac{\bar X-\mu}{S/\sqrt{n-1}...
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The product rule of probability - Specific rewriting

So, the product rule of probability states $$ p(X,Y) = p(X|Y)*p(Y) $$ In general for any set of variables: $$ p(X_1, X_2, ..., X_N) = \prod_{n=1}^N p(X_n|X_1, X_2, ..., X_{n-1})$$ ...
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Intuition about a coupon problem were we ask for the distribution of the unique coupons when the number of draws is fixed

Alternative viewpoint of the coupon collectors problem In the coupon collectors problem we draw from a collection of $n$ coupons, with replacement and ask the question how many draws $K$ it takes to ...
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1answer
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Expectation of a function of random variables

I'm trying to simplify the following expectation so that I can later solve a maximization problem: $max_k E[(A - kB)^2]$, where $A$ ~ $N(0,\sigma^2_1)$, $B = A+ \epsilon$ and $\epsilon$ ~ $N(0,\sigma^...