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0answers
7 views

Unique combinations of 7 items (repetition allowed, order doesn't matter) [migrated]

I am trying to calculate the number of unique combinations for a 7 element set with repetition allowed where order doesn't matter. For example: ...
0
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4answers
40 views

Variance of linear combinations of correlated random variables

I understand the proof that $$(aX+bY) = a^2Var(X) +b^2Var(Y) + 2abCov(X,Y), $$ but I don't understand how to prove the generalization to arbitrary linear combinations. Let $a_i$ be scalars for ...
0
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0answers
16 views

Combining unbiased hit rates

I am analysing data on an emotion perception task, where participants must decide if a given face is happy, sad, angry or fearful (essentially a forced choice between 4 options). I am confident that ...
3
votes
1answer
58 views

How to combine data several studies with events?

I have a compilation of following data on 10 studies, all of which had 2 groups: a control group which received usual treatment and an active group which received an intervention. The subjects were ...
0
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1answer
34 views

Arranging numbers

I keep on having problems with the same kind of questions involving combinatorics. This is one such problem where I am stuck. A bag contains 9 discs labelled 1 to 9. Andy chooses 4 discs at ...
3
votes
1answer
112 views

PCA: Eigenvectors of opposite sign and all eigenvectors are zero in R

I'm learning PCA in R language. I met two problems right now that I don't understand. 1) I am performing a PCA analysis in R on a 318×17 dataset using some custom code. I take eigen function in R ...
4
votes
1answer
61 views

Number of combinations with elements from different sets

Unfortunately I could neither find nor develop a closed formula, but I believe there is a simple solution for this problem. Could you please help me? Suppose that there are 4 different sets: Set A, ...
1
vote
1answer
94 views

Combination of two SVM Kernels

According to the book "Support Vector Machines" from Cristianini and Shawe-Taylor, it is feasible to make kernels from kernels. My question is now more in application of this methods with tools like ...
2
votes
0answers
26 views

Total probability distribution of multiple random lotteries

My question: Imagine $d$ identical lotteries. Each individual lottery picks a cost $c_{i}$ between $0$ and $1$. Picking a costs occurs with probability distribution $f(c)$. The total cost of these ...
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0answers
15 views

Combinations conceptual confusion

Suppose we toss a fair coin 43 times. What is the number of cases where number of heads > number of tails? I'm doing this like this: we'll have a satisfactory case only when number of heads are 22, ...
1
vote
1answer
31 views

What is the meaning of averaging combinations of independent random variables?

I'm getting into the management of multiple independent random variables in determining expectation and variance, but cannot see where averaging of a linear combination of independent random variables ...
1
vote
0answers
46 views

Probability of selecting exactly 2 members of a group of 7, out of 35 people, if 3 people are picked

There are 7 friends A, B, C, D, E, F, and G that belong to a classroom of 35 students. Three students are chosen from the 35. What the probability that exactly two of the group of friends is chosen? ...
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0answers
19 views

How many different arrangements, when selecting 2 out of 5 objects? [closed]

How many different arrangements are there, when selecting 2 out of 5 objects? In this question what should I use - nPr or nCr?
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3answers
1k views

Roll a 6-sided die until the total $\geq M$. Mean amount by which $M$ is exceeded?

Here is the question: You roll a fair 6-sided dice iteratively until the sum of the dice rolls is greater than or equal to M. What is the mean and standard deviation of the sum minus M when M=300? ...
5
votes
2answers
65 views

Sum of binomial coefficients with increasing $n$

Is there any formula for calculating $$\binom{n}{1} + \binom{n+1}{2} + \binom{n+2}{3} + ... + \binom{n+m}{m+1}$$ I have tried iterative method but is there any constant time method exist.
0
votes
0answers
29 views

how to calculate probability of a single member of a group having three characteristics/pre-conditions

In a study there are 72 members of a group A. How can I find the probability that any one member has all three of the following characteristics given what was known about the 72 members at the start ...
0
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0answers
46 views

combining samples from different gamma distributions normalized by means

I'm trying to figure out what to do with some experimental data from a psychoacoustic experiment. The data come from multiple subjects and are approximately gamma distributed; I am treating them as ...
1
vote
0answers
27 views

Probability of paired combinations

There are 8 friends: Alfred, Alex, Billy, Barbara, Connie, Chris, David and Donna. The friends are paired up at random. What is the probability that at least two pairs will share the same first ...
3
votes
1answer
177 views

What's the intuition behind combinations for coin flips?

Intuitively I understand something like "10 choose 3" as someone holding out an opaque bag containing 10 different objects and asking me to put my hand in and then instructing me, "from the 10 choose ...
1
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1answer
53 views

Variation on the urn problem and frequency distribution

I have $6$ machines each producing different coloured balls. The balls are mixed together in a large vessel. Groups of $6$ balls are extracted at random for packing. Each pack will therefore have a ...
5
votes
2answers
120 views

Distribution of linear combination of OLS regression coefficients

I have a simple linear OLS regression $Y_i = \alpha+ \beta_1 X_{1i} + \beta_2 X_{2i} + e_i$ where $e_i \sim N(0,\sigma)$. I have estimated the regression from the data and obtained estimates for my ...
2
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0answers
129 views

A smarter way for evaluating combinations of samples to optimize an overall score

I have the following problem (which I simplified for clarity) that I want to find k out of n samples (here: rows) that yield the maximum score (sum of the values in ...
4
votes
0answers
65 views

Combination of letters: some repeated letters

So I was looking for an answer on this assignment we have to program but I cannot find it anywhere. I'm a computer science student, not a statistics students. (And it isn't even for a statistics ...
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votes
1answer
314 views

All possible Combinations of 5 variables that can take 3 values

I have five variables which can take three values as shown below V1 = {1,2,3}, V2 = {1,2,3}, V3 = {1,2,3}, V4 = {1,2,3}, and V5 = {1,2,3} Then how many rows ...
0
votes
1answer
20 views

How to combine clinical variables?

I am dealing with several clinically used variables that are not linked to each others. Those variables are correlated to worsened prognosis (some are numeral and asymmetric, therefore correlations ...
0
votes
0answers
37 views

How can I combine positive likelihood ratios?

I only have the positive and negative likelihood ratio, sensitivity and specificity for four diagnostic tests. How can I add them or combine them to obtain likelihood ratios? I do not have the ...
0
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0answers
18 views

How to combine diagnostic tests with only sensitivity spec, PLR and NLR

Hi ive looked at the other questions but this ones seems to be different as i only have the test results from different clinical exams in the way of sensitivity, specificity, PLR and NLR ex: facial ...
2
votes
1answer
44 views

Combination/permutations question where repetition is allowed

So I guess this is a combination/permutations question where repetition is allowed. What is the % chance that six six-sided dice will show at least 3 duplicates of the same number or that there will ...
0
votes
1answer
50 views

combining subjective probability estimates and statistical estimates for forecasting

At the end of the year forecasters usually struggle year to predict landing estimate for the financial year due to variety of reasons including volatility, unreliable demand projections, inventory ...
4
votes
1answer
54 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
119 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 ...
1
vote
2answers
99 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?
0
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0answers
73 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
35 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
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2answers
95 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
51 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
270 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 ...
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0answers
51 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
28 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
78 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 ...
1
vote
3answers
193 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
votes
2answers
504 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
191 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
197 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
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1answer
266 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
369 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 ...
7
votes
1answer
117 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
100 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
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1answer
253 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
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0answers
122 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 ...