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

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Calculate similarity of probability vector and TFIDF vector

I want to compute the similarity between documents of two groups of documents. All documents have the same term vector of length 100, but documents in group A are probabilities, whereas documents in ...
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1answer
35 views

What is the probability of randomly picking 4 consecutive ladies out of a team of 11 people?

I was running the morning standup this morning and in contrary to the usual alphabetical order I announced I was going to go in "random" order today, however I then ended up giving all the ladies of ...
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1answer
27 views

Probabilistic Density

Variable $X$ has the following probability density: $f(x) =$\begin{cases} 0, & \text{x ∉ [0,2]} \\ kx(2-x), & \text{x ∈ [0,2]} \end{cases} How can I find the parameter $k$ so $f(x)$ is a ...
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2answers
31 views

Densities and Cumulative Distribution Functions

Has anyone seen this notation before? What does it mean? $\int_{0}^{\infty} f(x) G(x) dx$ $f(x)$ is a density and $G(x)$ is a cumulative distribution function
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12 views

How to compute the variance-covariance of log binomial distributions

I have some problems computing the variance and covariance of log binomial distributions. If $A \thicksim binomial(\theta,n)+1 $ and $B \thicksim binomial(p,A)+1$ (where $+1$ is added to avoid ...
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8 views

probability that noone will have to wait for change

This is the exact question text: $2n$ children are waiting in a queue for movie ticket. Tickets are priced at a quarter each. Each child pays for the ticket either with a quarter or with half dollar ...
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3answers
113 views

Why does the number of continuous uniform variables on (0,1) needed for their sum to exceed one have mean $e$?

Let us sum a stream of random variables, $X_i \overset{iid}\sim \mathcal{U}(0,1)$; let $Y$ be the number of terms we need for the total to exceed one, i.e. $Y$ is the smallest number such that $$X_1 ...
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1answer
33 views

Probability that 2 out of 3 friends win a raffle?

Let's say it's me and 2 other friends are at a raffle. There are 10 total participants. 3 of the 10 of us will win something, I don't care about what we win. A person can't win more than once. What is ...
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0answers
48 views

Urn with balls of two colours with a priori probability of each ball

If we have a urn with $N$ balls of two colours ($D$ red and $N-D$ black balls respectively), then probability of having $k$ red out of $n$ balls drawn at once without replacement follows the ...
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1answer
27 views

How to find the probability that a group of people is not allowed to enter a country given some factors?

I have this scenario: There are two countries A and B. A sends a group of N people to B... There is an independent probability of p that a person gets fatigued while traveling to B. And I have ...
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11 views

find probability of occurrence of events from a matrix and populate it to another matrix

I have a matrix as following that shows the actions and current states and next states in a Markov model. ...
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1answer
22 views

Probability of median > 1.5

I was asked a probability question: Given three numbers i.i.d as $\text{uniform}(0,2)$, what is the probability of the median greater than $1.5$? My hunch is that each number has $P(X > 1.5) = ...
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27 views

Failure in second Borel-Cantelli lemma without indepdence

I know that we can have events $A_n$ such that $\sum P(A_n)=\infty$, but $P(A_n i.0.) > 0.$ Is it possible that zero is actually achieved?
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1answer
34 views

Statistical reasoning in board game [duplicate]

In each round of the board game "The Resistance" three players are randomly and secretly chosen to be spies while the rest of the players are part of the resistance. The spies are then made aware of ...
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20 views
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1answer
17 views

Parameters in distributions

When it comes to representing certain continuous distributions like Gamma or Exponential, some books use the notation (1/theta)×e^(-x/theta), while other books use the notation theta×e^(theta×x) ...
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29 views

Proof of inequality [closed]

Can any one help me to prove this question: Let B ⊂ F be a sub σ-algebra inequality (|x||y|)/αβ ≤ x^2/(2α^2 )+y^2/(2β^2 ) with αβ>0 to prove E{|xy||B}≤αβ
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1answer
62 views

the likelihood of being one of three daughters and then having three daughters

I am not a statistics person myself, so I don't know of a more technical way to word it, but let me explain what I'm trying to get at. I am one of three biological children, all female. No other ...
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0answers
21 views

Find the CDF of a random variable given its relationship to a second random variable? [closed]

Take a lifetime with the CDF $F(t)=1-(1-t)^n$ for $t$ in $[0,1]$ and some natural $n$. Now find the CDF of the variable $T_x=T-x$ when $T>x$ for $x$ in $(0,1)$. I need help getting started on this ...
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1answer
41 views

Interchanging limit and derivative for CDFs

Let $F_{\theta}(x)$ denote a cumulative distribution function indexed by the parameter vector $\theta$. Given this definition is the following equation correct (and if so under which conditions)? ...
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2answers
93 views

Problem understanding the following probability problem

I have 120 blocks. Each block is one of two different materials, 3 different colors, 4 different sizes and 5 different shapes. No two blocks are exactly the same of all four properties. I take ...
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2answers
32 views

Conditional probability of a single random variable

I have a Gaussian random variable $X$ and I have been told to find $P[x < a | x > b]$ and $P[|x|>c]$. What does $P[x < a | x > b]$ mean in terms of a single variable? Is ...
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0answers
19 views

Probability of Red in a roulette after 100 blacks [duplicate]

Ignoring the 00 in a roulette, there is a 50/50 chance to get the ball on a Red result. Even after 100 times it's Black the probability will be the same. However, if I were to bet on the next one, it ...
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1answer
233 views

Is the following statement for variance true?

I know: Let be $X$ a random variable and $c\in\mathbb{R}$. Then is $$Var(cX)=c^2Var(X).$$ But is it true that $$Var(cX)=\underbrace{Var[Var[\ldots Var}_{c \text{ times}}[X]\ldots]]?$$
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26 views

Predict the average stay of customers

This is my data: customers subscribing to a service and more or less regularly having activities on that service. I want to calculate an average length of stay for the customers using the service. I ...
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2answers
47 views

How many combinations of K ordered numbers from N numbers list

I have N numbers, 1-N (my N is 70). I need to know how many combinations of sequences of K numbers (K is 8 in my case) are possible, where the sequence is always increasing. Examples: ...
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17 views

Neural network + probability distribution modeling

I'm having A training set $(a^i_1, a^i_2...a^i_n, t)$ I also have a probability distribution over $a_k$ and $t$ I need to use a neural network in order to find an aproximation. How can I include ...
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20 views

Sequential hypothesis testing with independent but non-identically distributed samples

I want to apply the hypothesis for my problem. According to A. Wald regarding sequential hypothesis, he used independent and identically distributed (iid) observations or samples but in my case my ...
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32 views

When to assume that $\Pr(X=x, Y=y) = |\mathcal{Y}|^{-1} \Pr(X=x|Y=y)$?

Background Let $\mathcal{X} = \{x_1, x_2, \ldots, x_n\}$ be a set of samples, each that corresponds to a label in the set of labels $\mathcal{Y}$. Ideally, our objective is to find the joint ...
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2answers
94 views

Combining Binomial Random Variables

(Disclaimer: This is not a homework question). I am trying to teach my self some elementary probability, and I thought of this following example: Imagine you are playing a game involving two coins. ...
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3answers
29 views

Conditional Probability vs Joint Probability - Disease and Positive Test example

I was reading this example about finding the probability of one actually getting the disease, after he is diagnosed positive by a test, as he is determining whether or not to proceed with treatment as ...
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1answer
28 views

Normal Probability Plot of Residuals

Below is a normal probability plot of residuals from my lecture The NSCORE(z score) is quite confusing. For example, the first nscore is -1.54664, which should be 0.061 or 61% percentile, it doesn't ...
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1answer
24 views

How to calculate $P(A)$ given only $P(A|B)$ , $P(A|B')$ and $P(B)$?

Assume $A$ and $B$ are two dependant events with only the following details provided $P(A|B)$, $P(A|\neg B)$ and $P(B)$ How to calculate the value of $P(A)$?
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1answer
41 views

What is the probabilistic view on clustering? [closed]

Say that we got a set $\mathcal{X} = \{x_1, x_2, \ldots\}$ of samples. You want to partition $\mathcal{X}$ into $k$ subsets, where $k$ is unknown besides the fact that $k \ge 1$. How clustering ...
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3answers
290 views

Expected value of sum of cards

If each card on a regular 52 deck card has points that corresponds to their number (like 2 of hearts is 2 points, 7 of clubs is 7 points), the Jack, Queen, King each being 10 points and you keep ...
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0answers
35 views

Expectation of $|U|$ given the first and second moments of $U$

Let U be a random variable with $E(U)=0,Var(U)<\infty$, is it true that $E(|U|)<\infty$?
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1answer
43 views

Find cumulative probability from given formula

Given a formula to calculate instantaneous probability of an event. f(i) = 0.0222 * e ^ (-­i / 11.5) For instance 0.0222 * e ^ (­-4 / 11.5) is the probability of ...
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1answer
97 views

Distribution of $|q|^2$ if $\Re[q]\sim \mathcal{N}(\mu_1,\sigma^2/2)$ and $\Im[q]\sim \mathcal{N}(\mu_2,\sigma^2/2)$

Let $q$ be a complex random variable such that: $\Re[q]\sim \mathcal{N}(\mu_1,\sigma^2/2)$ and $\Im[q]\sim \mathcal{N}(\mu_2,\sigma^2/2)$. What is the PDF and CDF of the squared norm $|q|^2$ ?
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15 views

How difficult is it to collect the full set of toys from McDonald's Happy Meal? [duplicate]

Say there are 12 different kinds of toys available and you don't know which one you'll get as a free gift when you buy a Happy Meal. How many Happy Meals do you have to order before you can collect ...
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1answer
57 views

Calculating the probability a predicted point is 0

I have a deterministic function $f(x)$ and have evaluated some points $x_1,...,x_n$. So essentially I have pairs of data $(x_1,f(x_1)),...,(x_n,f(x_n))$. I am modeling the function $f(x)$ using a ...
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1answer
53 views

How should I calculate the variance of a circular random variable?

Consider the following function being the PDF of a circular random variable (orientation angle from the zenith) ...
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44 views

References that justify use of Gaussian Mixtures

Gaussian mixture models (GMMs) are appealing because they are simple to work with both in analytically and in practice, and are capable of modeling some exotic distributions without too much ...
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18 views

In layman's terms, what is the difference between likelihood and probability? (discrete mathematics)

Also, what is the difference between with and without replacement when solving for both likelihood and probability. I have seen that when it is without replacement, there is a denominator, why?
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23 views

Positive dependence and functions of random variables

Is there a notion of positive dependence such that if $X_{1},\dots,X_{n}$ are positively dependent, then for any two functions, $a\left(X_{1},\dots,X_{n}\right)$ and $b\left(X_{1},\dots,X_{n}\right)$, ...
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1answer
32 views

Standard deviation for probability (multiple choice)

In a multiple choice test with 4 answer options, the probability of guessing correct is 25% (assuming you have no knowledge about the materials at all). Thus, regardless of sample size, my estimated ...
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12 views

how to know if the observed overlaps in independent sets is significant?

I have a list of names ( derived from a statistical test ) that overlaps with a list of names ( set2 ). I generated a random list of names ( random ) and overlapped with set2. How do I know if the ...
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15 views

Regression to the mean with correlated and cumulative past

My colleagues and I are posing this question to our intro statistics students, but are in disagreement about the answer: Suppose a student always got scores far above the class average throughout ...
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22 views

How to add time estimates

Imagine I have a bunch at tasks to complete sequentially. There is some uncertainty about how long each task will take to complete. So for each task, we might estimate a 50% chance that it can be ...
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1answer
46 views

De Méré's Paradox - Probability of getting at least a “six” with 4 throws

I was reading about De Mere's paradox examples, where he incorrectly assumed that the probability of getting at least a "6" by throwing a dice 4 times is 4(1/6) = 4/6 However, when I was looking at ...
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31 views

Decision Theory

Patient X is worried that he may have disease Y. He goes to a doctor who performs some test and based on the test determines that the probability that X has disease Y is 0.3. The insurance company has ...