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

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Forecasting if the next number is higher or lower

how will I know (or are there any math formulas) if the next number will be higher or lower based on a given set of numbers? Like: 46,73,29,12,04,27,28,81,62 - Next number is higher or lower? I'd ...
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1answer
17 views

Probability two people arrive at the same time?

Two people arrive at a train station at a random time between 12pm and 1pm. They arrive independently of each other and their arrival times are uniformly distributed. What is the probability they ...
3
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2answers
32 views

Inequality of binomial probabilities

I need to show the following: I have two binomial random variables $X \sim BIN(m,p_1)$ and $Y \sim BIN(m,p_2)$, where $p_2 \geq p_1$. I want to show for any fixed constant $c \in \{0,...,m-1\}$ that ...
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2answers
202 views

Is the logarithmic transformation sufficient to tame every distribution?

Today I realized a quite known fact. The log transformation of a random variable, drawn from a fat tail distribution, maps into an exponential tail distribution. ...
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1answer
103 views

How to calculate one probability out of several Bernoulli probabilities?

For a multi-agent problem I want to calculate the probability that a certain event happens for any agent (1 or more). There are n agents, and $P(X_i=1)=p_i$ for each agent. I want to calculate the ...
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1answer
18 views

Combining two probability scores [duplicate]

This question is rather mathematic, and I am quite sure some theory should already exist but I can not find it... Say I have some data records, and for a certain record X two independent statistical ...
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15 views

Probability Independent events

I am currently doing an online statistics course for my program. I am stuck on one question where it is asking me to determine if the two events are independent. I would like a confirmation from those ...
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0answers
8 views

Non Homogeneous Poisson Process Insurance example [on hold]

An insurance company finds that for a certain group of insured driver , the number of accidents over each 24 hours period rises from midnight to noon and then declines until the following ...
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0answers
18 views

Two-alternative forced choice [on hold]

Suppose that $p[r|+]$ and $p[r|-]$ are both Gaussian functions with means $\langle r \rangle_+$ and $\langle r \rangle_-$ and common variance $\sigma_r^2$. How can I show that $$P[correct] = ...
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1answer
14 views

Learning the joint probability distribution of 3 variables from partial observations

I have a dataset composed of 3 random variables X, Y and Z. However, at each sample one of the random variable remains hidden. As an arbitrary example, the observation 1 is $(x_1,y_1)$, the ...
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0answers
21 views

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
44 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
30 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
35 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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0answers
17 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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0answers
12 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
144 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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2answers
47 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
49 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
30 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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0answers
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
24 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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0answers
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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1answer
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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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31 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
64 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
95 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
33 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
20 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
236 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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27 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
48 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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0answers
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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0answers
21 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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0answers
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
97 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 ...
3
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1answer
29 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 ...
6
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2answers
294 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 ...
4
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1answer
101 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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0answers
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 ...
0
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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 ...