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

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What is the probability of Stock B having a return less than 6%? [on hold]

What is the probability of Stock B having a return less than 6%? Facts: 15% average return for the holding period, standard deviation of 9%.
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3answers
87 views

Can PMF have value greater than 1?

Can a Probability Mass Function can have value greater than 1 like we have in Continuous functions(pdf) and why? Please give 1 example if the answer is yes. And If the answer is no then why PDF can ...
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How to uniquely identify each Employee in an Organisation with a hash value between 0 and 511 [on hold]

let I be a set of random input values, with I = N . Then h meets this quality criterion if (∀1 ≤ i ≤ n)(|h(I) ∩ Pi| ≈ N/n ) if N >> n. Suppose you want to use Employee numbers to calculate a hash, ...
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18 views

Naive Bayes Assignment of Feature Probability

I'm using the .show_most_informative_features() function from NLTK's Naive Bayes to generate features to be used with a lexicon. In the case of my binary-classification problem, these features are ...
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1answer
37 views

How to interpret the importance for a regression coeffcient in Bayesian regression from its posterior density?

I am trying to interpret the regression coefficients of a covariate in a Bayesian linear regression problem. More specifically, I am trying to determine if the regression coefficient have an important ...
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23 views

Unsure about the distribution of the canonical statistic

Iam a bit unsure if the distribution of the canonical statistic below is correct ? I suspect i would need idenpendent variables to show the correct answer. Let $Y_1,Y_2,...Y_n$ be a sample form a ...
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0answers
12 views

Find the Expected Value of the Sum of Random Variables [on hold]

R is discrete random variable defined by the density function: $f(n)=a\frac{2^n}{n!}e^{-2}$ when $n\geq 0$; $f(n)=a3^n$ when $n<0$ Random variable $T=X$ if $R\geq 0$; $T=0$ otherwise. $a$ is ...
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2answers
393 views

How to interpret Bayesian (posterior predictive) p-value of 0.5?

In the following paper found here and reference below, the author suggests that "if the model is true or close to true, the posterior predictive p-value will almost certainly be very close to 0.5" . ...
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0answers
10 views

How to calculate the probability with replacement

I have the following numbers in an urn: 1 1 2 2 3 and the problem specifies that we make 2 draws randomly with replacement. First, I want to calculate the ...
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1answer
22 views

Combination question with and without replacement

There is a group of N unique things. A simple random sample sub group x can be taken without replacement where the number of samples is x, x < N and x = 25% of N. The sample sub group x is replaced ...
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0answers
24 views

Predicting elections with a random sample

If I have a population of exactly 100.000 voters, and I know they all voted in either candidate A, B, C, D or E. (e.g where the results of a random sample of 100 voters are A = 40%, B = 30%, C = 10%, ...
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26 views

Which test should I use? Help!

I'm new here in the group, so I do not know if I'm putting my doubt in the correct place... :) I am conducting my master's thesis, and I came across a problem in the analysis of my results... In my ...
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1answer
21 views

Proof the joint bivariate cumulative distribution function

I would like to proof the expression ($P[X>x, Y>y]$) for two continuous random variables $X$ and $Y$. $P[X>x, Y>y]$ = $1- P[X \leq x, Y \leq y]$ (From the definition of probability). (...
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0answers
12 views

Probability calibration metric for multiclass classifier

A machine learning classifier can be calibrated so that when the probability that datapoint i is of class A is 0.6, this is true 60% of the time. In the binary class setting, this can be visualised ...
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0answers
31 views

Hypothesis test for machine failure rates

Let's say I have one collection of machines (made by manufacturer 1). These machines run over a few days and fail at a certain rate. Let's say they run for a total of $h_1$ machine hours and the ...
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0answers
21 views

Probability of observing certain data given prior knowledge

Background: I am building a framework to analyze a type of experiment called protein microarray. The basic idea is that you can affix a bunch of different proteins on a microarray chip and then apply ...
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0answers
18 views

Probability of stale cache hits w/ exponentially distributed read and write inter-arrival times

I am trying a create a model for a very simple system which consists of a server and 2 clients: R and W. The server stores a piece of data D and hands out leases for caching D on the clients. The ...
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0answers
12 views

Probability of Finding Two Matching Subsequences in a Sequence

I'm currently studying DNA sequencing and am trying to find a formula which gives the probability that a subsequence of length $k$ appears twice in a sequence of $L$ bases (characters); this is pretty ...
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1answer
20 views

Candidate Sampling for Softmax - Tensorflow; Sampling Probability

I am trying to understand the mathematics behind the sampled softmax in Tensorflow. They have the following document, trying to explain how the sampling process works: https://www.tensorflow.org/...
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1answer
30 views

Combining probabilities for multiple individuals

Take the example question, 'How many individuals will be in state A'. Let's say I have 5 individuals each with a probability of entering state A. Those probabilities could be ...
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2answers
50 views

True probability vs estimated probability

Is it correct to think that the true probability of an event cannot be ever known? When studying probability, in the first lectures, there are those typical exercises which start with sentences like: ...
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0answers
17 views

Statistics Question [on hold]

Phalaborwa Development Corporation (PDC) has purchased land that will be the site of a new luxury double storey complex. The location provides a spectacular view of the surrounding countryside, ...
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1answer
13 views

How does an increase of the correlation coefficient of the sample affect the p-value?

I don't quite understand the explanation of an answer in my textbook. Data are collected on the height of a cake and the temperature. When a hypothesis test is conducted to test for positive ...
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27 views

Probability distribution model

I have a dataset in the following form: ...
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0answers
15 views

What is the expected fraction of observations in the top x% that remains in the top x% after a random shock?

I'm struggling with a probability question, and I was hoping someone here could help me out. Here's the setting. Suppose you draw observations from a probability distribution Z and sort these ...
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0answers
16 views

Truncation and a composite distribution

Suppose $X$~$N(a,1)$ $Y|X$~$N(X,\sigma^2)$ Then what is $X|Y<0$ ~ ? and $E[X|Y<0]$ ~ ?
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17 views

Independent Probability Question

This is a question I've been trying to solve. A certain person considers that he can drink and drive: usually he believes he has a negligible chance of being involved in an accident, whereas he ...
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1answer
40 views

A special case of the law of large numbers for (possibly) dependent, identically distributed random variables

I want to show that $\dfrac{1}{N}\sum\limits_i^N x_iw_i \to 0$ as $N\to\infty$, where $w_i\sim \mathcal{N}(0,\sigma^2)$, $\mathbb{E}[x_i] = 0$ and $\mathbb{E}[x_i^2] = \rho$. The $x_i$s are ...
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1answer
47 views

Probability Related [closed]

There are 300 students in an online MBA program for working professionals, for whom the attendance in online classes is 70%, i.e. on an average, 210 students are present in an online session. Fifty ...
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0answers
13 views

Imputing missing data with MICE where each observation has different levels

I have a set of observations that each consists of different levels. For example, I ask a $P$ individuals $N$ questions, each question with a possible $k_n$ discrete responses. This produces a table ...
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2answers
69 views

Odd Number Probability

How do I calculate the probability of randomly picking a number in the range from 0 to 10000 where exactly two of the digits is odd. For ex 5001 or 1010 etc.. and how would I do the same calculation ...
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0answers
18 views

Predicted probabilities for multiple categories of a categorical variable

I'm developing predicted probabilities for hypothetical cases in my glm (binary logit). I have a four category categorical predictor where "Single" is the reference category and "MOU", "JPA" and "AD" ...
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60 views

How were statistical distributions discovered?

Let me start, that i know that it's not very difficult to generate a probability distribution. If one takes any positive integrable function and normalizes it, this results in a probability density. ...
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CLT for different but independent random variables [duplicate]

Is the Central Limit theorem still applicable if we consider a sum of independent but different random variables? (Each with finite mean and variance) Is there some theorems about this ?
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2answers
38 views

3 D6 pick 2 vs 2 D6 with 1 reroll

I was wondering if there is any statistical difference between rolling three 6 sided dice and taking the best two (looking for a 7 or higher) and rolling two 6 sided dice with the option to re-roll ...
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1answer
23 views

Markov inequality

Suppose, $X_1,X_2,\ldots,X_n$ be i.i.d. r.v.s such that $P(X_{n}=e^n)=\frac{1}{n^2}$; $P(X_{n}=0)=1-\frac{1}{n^2}$ Therefore, show that $X_{n}$ converges to $0$ in probability. Ans: By, Markov ...
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0answers
16 views

How to calculate PMI when P(x,y) = 0?

I'm trying to calculate PMI using probabilities estimated using binary occurrence counts from a set of documents. In short: $P(x)$ = # documents x appears in / # documents $P(y)$ = # documents y ...
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0answers
12 views

Introducing “Unclassified” class into a multiclass classifier

I'm trying to multi-class classification problem with a small addition that I can't find a decent way to handle: according to domain knowledge, no classification is better than a wrong classification. ...
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1answer
45 views

Writing a conditional probability as a marginal

So I understand that using sum-rule one can write a probability as a marginal: \begin{equation*} P(x) = \int{P(x,\theta)d\theta} = \int{P(x|\theta)P(\theta)}d\theta \end{equation*} But how is this ...
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1answer
37 views

Is there a metric of representativeness in statists?

In a group of 1000 people, where each of them is either A, B, C, D or E (no one can be more than one thing). If I have exactly 200 people with each trait (20% per trait), when I take a random sample ...
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1answer
32 views

Probability Distribution and Transformation

Let X have the following distribution function F(x)= 0 for x<0; x/3 for 0<=x<=2; 1 for x>2. Let Y=X^(2) To find P(Y<(X)) Do we simply substitute X^2 for Y and divide to get P(X<1) ...
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0answers
24 views

Dilemma concerning prediction of user satisfaction

Imagine that you have data with information about users : Age, sex, location, etc ... with the answer to two additional questions : Q1 = Have you tried product P ? yes/no ; Q2 = Did you enjoy product ...
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0answers
18 views

Probability model EV

I'd like some help setting up a probability model and determining it's EV, but I don't really know where to start. Say there are 6 ranks, beginning at 0 and ending at 5. For each rank ...
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1answer
33 views

how to solve this markov chain problem?

This is a problem in the book of "introduction to stochastic process ". Any help to solve this problem ??
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1answer
24 views

Finding probability

*Suppose it is known that in a certain population 10 percent of the population is color blind. If a random sample of 25 people is drawn from this population, find the probability that 5 or fewer will ...
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0answers
20 views

Solving fraction value using Gamma function

How is Γ(3.3) = 2.68? I have tried using various formulas, but couldn't reach the exact value. Thanks for the help in advance!
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1answer
24 views

How to find the maximum probability of an hourly based variable ?

Let's say my dataset is composed by the time (hour) of when a user uses his TV, over a month. I may have something like this : ...
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1answer
33 views

Probability based on Observed Data

I'm trying to figure if my reasoning and application of probability is correct in this made up example using R. Example data: ...
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1answer
41 views

Distribution vs Distribution Function

I am currently reading through Elementary Stochastic Calculus with Finance in View and I am going through the probability review section. Intuitively I know the difference between a Probability Mass ...
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0answers
19 views

Discrete version of multivariate normal distribution

Let's say that I have a 2d map, and I would like to explore around my house. Drawing samples from a bivariate gaussian centered at the x, y location of my house makes sense, as I don't want to stray ...