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0answers
8 views

Fewest weight possible of the balls [migrated]

You are given 4 balls, all equal in weight except for one that is either heavier or lighter. You are also given a two-pan balance to use. In each use of the balance you may put any number of the 4 ...
4
votes
1answer
41 views

Getting $k$ consecutive heads

If a coin is tossed 3 times, there are 8 possible outcomes: $$\text{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}$$ In the above experiment we see 1 sequence has 3 consecutive H, 3 sequences have at ...
2
votes
1answer
103 views

drawing balls from an urn

Suppose there are 7 golf balls in an urn and you draw balls in 3 stages without replacement. First you draw 2, then 3, and then the remaining 2. How many ways are there to do this? I believe the ...
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vote
2answers
90 views

Sum of combination

My problem is: Evaluate: $$\sum_{i=0}^n i{n \choose i}$$ I only know that $$\sum_{i=0}^n{n \choose i} = 2^n$$ not so sure when an "i" is added. What is the step of this evaluation?
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0answers
23 views

Significance of linear combination of two insignificant regression parameters

I'm running a model with an interaction term, of the general form: $Y=b_1X_1+b_2X_2+b_3X_1X_2$, whereby $X_2$ is a dummy variable and $X_1$ is continuous. Neither $X_1$ nor $X_2$ turn out as ...
2
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0answers
28 views

Co-occurrence statistics for sets

I am looking for help in the following situation: I have a set of numbers $A=\{1, 2, \dots, 100\}$, and I am drawing subsets of 10 of these numbers $\{a_1, a_2, \dots, a_{10}\}$ according to an ...
3
votes
2answers
75 views

Estimating total number of people from an observed sample

The well known "German tank problem" shows how to answer the question: "If I have tanks which have an increasing serial number, and I see a sample of tanks and record their serial numbers, what is the ...
2
votes
1answer
40 views

probability of tally having a count of 0 in x variables after sampling with replacement

I am a non-statistician testing a randomising algorthm. If I have a sample of size 100 (numbered balls) with replacement and that 50 such samples are independently drawn. To my understanding, the ...
2
votes
1answer
75 views

Combining outcome measures for meta-analysis

I have to conduct a meta-analysis. Following problem occured: a single study have measured Quality of Life and therefore, used two questionnaires. Now is my question whether I have two choose one of ...
0
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0answers
34 views

Extract knowledge from the (possible unrelated) combination of multiple data sets

I am a beginner in this area so please bear with me. I have 2 data sets: information about the cars which were sold in particular area (cost, model, number of seats, manufacturer, etc.) information ...
0
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0answers
22 views

statistical distribution that would generate combination of numbers without repitition

I have set of 'n' numbers in an array. Is there a statistical distribution that would generate randomly picked 'n' numbers from the same array such that there are no duplication. For example, if I ...
1
vote
1answer
72 views

How many different ways can I arrange this committee?

A company has 20 employees, 12 males, and 8 females. Suppose we need to form a committee of 5 employees. How many ways are there to form this committee if we need 3 males and 2 females? I believe ...
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3answers
120 views

Combination of Data from Two Normal Samples not Normal?

I have two sets of data that hypothesis tests have shown to be normal and from the same distribution. I'm using MATLAB and for the way they give p-values, higher p-values suggest a better ...
0
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0answers
33 views

How to combine complete regression coefficients?

How I can combine hazards regression coefficient in meta analysis? I want to have a complete regression from combing hazard regression with different covariates. I mean some of them have additional ...
0
votes
2answers
221 views

Frequency of combinations possible

I have an SPSS data set with 700+ respondents and 13 products that they could own. Each product has its own variable Product01 = 1 means they own product 1 Product02 = 0 means they dont own product 2 ...
1
vote
1answer
99 views

How to combine likelihoods from multiple binomial trials. Can we also determine the overall FDR?

A king has rounded up 1000 people suspected of counterfeiting coins, which look and feel the same as the official coin. However, only the official coin is truly fair (Pr(heads)=0.5), while all fake ...
0
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1answer
92 views

Probability understanding 52 C 5

Hi I have a problem undertanding this: Example: In a deck of 52 cards, 5 cards are chosen. ...
3
votes
1answer
200 views

Combine several softmax output probabilities

I would like to combine the outputs of five neural networks, each with a softmax output layer of three classes each. A typical, example output is shown below:- where Figure 1 is the output of model ...
2
votes
3answers
242 views

How to combine time-series based features with different frequencies

I have 3 features which I want to use in my classifier. They are all time-series data-based. However, they are all at different frequencies and there have different matrix dimensions. I was wondering ...
5
votes
1answer
87 views

Co-occurrence of properties in a population

I have 150 properties that may occur in a population of 10000 people. Individual people may have none, one or a couple of these properties. The properties are not mutually exclusive and have different ...
1
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0answers
64 views

Bayesian belief network for finding combinatory effects of multiple environmental variables on allele frequency

I'm a beginner to Bayesian belief network (BBN). I read a few articles on introduction to BBN. So I know a general idea of BBN. But I'm struggling to construct a graphical network and conditional ...
2
votes
1answer
142 views

Correlations with a linear combination means correlation with individual variables?

I was having this conversation with someone, and I feel like I have an explanation, but would greatly appreciate if someone could verify whether what I'm thinking is just completely wrong. He made ...
1
vote
0answers
88 views

Patterns in binary sequences

I have data that looks like this: 011100111110100111 111111111111110010 111100001111000011 1D lanes of streams of data. Each row signifies the presence of a ...
1
vote
1answer
306 views

How to calculate the confidence interval of a function of a combination of two linear models

We have two linear fits, one for each data-set (unfortunately they include weights but I'm willing to ignore that if there's a nice analytic solution to this). Data-set ...
1
vote
1answer
115 views

How can I get annual rates of change for combined trend estimates?

I would like to combine trend indices (gained with different methods referring to the same subject, assuming they do not differ significantly) of two different time series and to derive the combined ...
1
vote
1answer
390 views

Combining results of two classifiers to better classify a data-point

Suppose that a classifier A classifies a data-point $x$ in class LA1 with probability PA1 and class LA2 with probability PA2 (with LA1 != LA2 and PA1>PA2); and that a classifier B classifies a ...
5
votes
1answer
251 views

Probability of independent events within a specified window

So I have an event that can occur on a daily basis with probabilty 1%. There is no dependence between days. Now I can calculate the probabality of the event occuring X times in Y days: ...
0
votes
1answer
114 views

Possibilities of variables combination and conclusion

I have 11 independent variables and one intercept. If I am right, that means there are $2^{12}=4096$ possible different models, right? So does this mean, if I calculate each model and save the ...
0
votes
1answer
122 views

Trying to Calculate Basic Lunar Probabilities

I'm trying to do what I thought was a basic problem but doesn't seem to be working out properly. I'm looking at disproving a claim that tides cause earthquakes, where the main mechanism that people ...
3
votes
1answer
93 views

Validity of using the mean duration across a sample period as the trial for Student's t test or Welch's test

Business Problem We are measuring the duration of an operation on our server. We want to know if certain changes (call them treatments) make this operation faster or slower. Data Our current test ...
1
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0answers
260 views

Combining probabilities for sports prediction

I use two criterion ($w$ and $x$) for predicting the outcome of football matches. Analysis of historical records has provided me with two best fit linear equations. The probability that the team ...
4
votes
1answer
383 views

Understanding Fisher's combined test

I am using Fisher's combined test to fuse several different independent tests. I have a problem understanding the results in some cases. Example: Let's say I run two different tests, both with the ...
3
votes
2answers
356 views

Calculating possible combinations with restrictions

I have five additives that can be mixed into a chemical. Each one can be mixed in at a discrete percentage from 0.02% to 0.22% of the chemical (i.e. 0.02%, 0.03%, 0.04%,...0.22%). Each additive must ...
0
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0answers
73 views

Unique subsequences of the human genome

I am working on a project involving genomes. I am going to divide a genome into subsequences, and then do something with those subsequences. I want to know if the subsequences that I produce are going ...
2
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2answers
5k views

Simplify sum of combinations with same n, all possible values of k

Is there a way to simplify this equation? $$\dbinom{8}{1} + \dbinom{8}{2} + \dbinom{8}{3} + \dbinom{8}{4} + \dbinom{8}{5} + \dbinom{8}{6} + \dbinom{8}{7} + \dbinom{8}{8}$$ Or more generally, ...
4
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1answer
1k views

Simple combination/probability question based on string-length and possible-characters

Assuming "complete randomness" and given a string with a length of 20 characters where each character may be one of 62 possible characters: What are the total number of combinations possible? ...
7
votes
3answers
867 views

What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?

If I am selecting 232 people from a pool of 363 people without replacement what is the probability of 2 of a list of 12 specific people being in that selection? This is a random draw for an ultra ...
1
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1answer
143 views

How many possibilities is there to choose 10 boxes of given size?

We have a collection of 40 boxes, each is one of four sizes (evenly distributed 10 of each): sizeA, sizeB, ...
2
votes
2answers
177 views

$E(\min_{1 \leq i \leq m} |x - y_i|)$

I have faced a statistical problem in a computational biology question. I will explain it in statistical language. Let's say we have the results of rolling one red die, $x$, and $m$ black dice ...
1
vote
1answer
136 views

Proof for a binomial equation

I'm trying to formally write out the problem: Light bulb color problem when I come up with the following equation ...
0
votes
0answers
78 views

What is the average expectation value of two specific objects in a queue?

I need some hand to solve this problem. Suppose a queue can be filled by three type objects (M, F and A). Depending on the number of each objects the line length can be different. We are looking ...
3
votes
1answer
1k views

Generating all possible unique combinations of dataset with two variables

I am fairly new to R and I have been reading all related topics but still I don't manage to solve my rather simple problem. I have a dataset with 5 cases for two variables (X,Y), for instance: ...
0
votes
2answers
89 views

Mathematical description of problem where sample is asked about three most liked brands?

I have a population of branded products lets say diary food and want to know which brand is the most liked. I ask 1001 people to tell me their three most liked brands. What is the mathematical ...
6
votes
2answers
486 views

How to combine the results of several binary tests?

First off let me say that I had one stats course in engineering school 38 years ago. So I'm flying blind here. I've got the results of what are essentially 18 separate diagnostic tests for a ...
5
votes
1answer
400 views

How to make a combination (aggregation) of quantile forecast?

Framework. Fix $\alpha\in ]0,1[$. Imagine you have $n$ $\alpha$-quantile forecast methodologies that give you, at time $t$ for look ahead time $t+h$, an estimation of the quantile of wind power. ...
4
votes
2answers
433 views

Probability of at least one unique outcome

We have n actors. Each actor chooses from n*2 actions. How can I calculate the probability that at least one actor will choose a unique outcome? For example, say we have 5 pickup artists in a town ...
4
votes
1answer
879 views

The “Risk” game dice problem

This definitely sounds like a homework, but I assure you that it's not. You're probably familiar with the Risk game. Now, friend of mine rolled 3 aces in one hand. I reckon that probability of such ...
4
votes
2answers
3k views

How can I obtain some of all possible combinations in R?

Sometimes I want to do an exact test by examining all possible combinations of the data to build an empirical distribution against which I can test my observed differences between means. To find the ...