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3
votes
0answers
12 views

State of the art for bagging/model averaging?

If I estimate a collection of models predicting $Y$ by $\hat{Y}$, which methods are out there to combine these forecasts? Which methods work well/best (and why?) to improve prediction accuracy? My ...
1
vote
1answer
15 views

Probability that 2 out of 3 friends win a raffle?

Let's say it's me and 2 other friends are at a contest. There are 10 total contestants. What is the probability that exactly two of us win (it's not ranked, so it's just a combination problem)? I'm ...
0
votes
0answers
10 views

R - splitting a vector into three groups, min size, order matters

Hello everyone and thank you in advance for your time. I am looking for the different combinations that could split a vector into three groups (high, medium, low), each group needs to contain at ...
3
votes
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: ...
1
vote
0answers
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 ...
0
votes
2answers
41 views

Variance of Gaussian linear combination

I have two independent gaussian distributions to combine and I have a doubt. Let's say we have $X \sim N(\mu_x,\sigma^2_x)$ and $Y \sim N(\mu_y,\sigma^2_y)$. I want to mix the two variables with a ...
0
votes
0answers
18 views

Sampling combinations

I'm running a simulation where the different inputs are combinations of $n$ values taken in $r$. The problem is that even though $n$ is small, the number of different combinations is very large, so I ...
1
vote
1answer
121 views

minimizing total travel time [closed]

Green circles are salesman and A-B-C are destination points. I need to move green circles so that total travelled time should be minimum and each salesman should go to a different point. So ideal ...
0
votes
1answer
23 views

Unique vectors that can result from bootstrapping

My question concerns the unique number of vectors that can result from bootstrapping. Ie I have a vector of length 12 with the following elements : 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 and I would like to ...
5
votes
1answer
107 views

The “strongest password”

I have an app which is protected by a four-digit-PIN and the user got five attempts at logging in before the account is locked. Now, one of my customers wants to "strengthen" the security and ...
0
votes
1answer
41 views

Tricky Question re Customer Purchase Probabilities

I would like to calculate some parameters relating to customer purchasing in a retail situation. I have some basic information which I can use: Customer visit frequency in the form of probability ...
1
vote
1answer
105 views

Which is the maximum number of combinations between two populations

I have two populations of size N1 and N2: pop1 = {a,b,c,d,e,f,g} and pop2 = {h,i,j,k,l} I want to produce combinations of this two populations swapping individuals between the two but keeping the ...
0
votes
0answers
16 views

How Can I Combine Multinomial Data from Survey with Two Parameter Univariate Distribution

I have survey data, $X$ that measures a variable on a 1-5 Likert type-scale. I have a second variable $Z$ which, given a suitable parametric assumption, I can identify the mean and the variance but ...
1
vote
1answer
81 views

Combining multiple outcomes in studies (no meta-analysis)

I'm looking for a way to combine effect sizes (mean difference) and variances for several single studies but I don't want to conduct an overall meta-analysis. That means I'm only looking for an ...
0
votes
0answers
12 views

How to calculate the total forecasted demand after forecasting demand of two types of clients seperately

I am trying to make a sales forecast with the ARIMA model. This business has two types of clients that have completely different buying behaviour. My idea was to separate them and make a sales ...
6
votes
3answers
322 views

What are the statistical methods I can use to find popular or common combinations of categorical variables?

I am doing a study on polydrug use. I have a data sets of 400 drug addicts, who each stated the drugs that they abuse. There are more than 10 drugs and hence there large possible combinations. I have ...
3
votes
1answer
58 views

Calculate the probability of observing n elements in m draws from an uneven frequency distribution, in order but consecutive or not

I want to calculate the probability to observe a certain sequence of n elements in order, but not necessarily consecutively, after drawing m times from an uneven frequency distribution. For example: ...
0
votes
0answers
16 views

Basic question about assigning items to groups

Suppose there are 9 items, which are assigned to three groups. The first group may contain 2 items, the second 3, and the last one 4. In how many different ways the items may be assigned to the ...
1
vote
0answers
30 views

Combining Forecasts: Best Information to Solicit from Forecasters?

Suppose Statistician $m=1$ produces a set of $h$-step-ahead point forecasts $\hat{x}_{t+h|t, 1}$ of $x_{t+h}$ where $x_{t+h} \in [0,1]$. Also, this point forecast could come with: a predictive ...
0
votes
1answer
34 views

Deck of Cards - Combination Question

The question asks to randomly draw 13 cards from a standard deck (52 cards). What is the probability that there are 3 aces in those 13 cards you drew. Let $n(s)$ be the number of $13$ card ...
1
vote
4answers
535 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
votes
1answer
30 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
92 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
votes
1answer
37 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
321 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
148 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
204 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
37 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 ...
0
votes
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
35 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
133 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? ...
1
vote
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?
10
votes
2answers
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
75 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
35 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
votes
0answers
87 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
2answers
136 views

How to program the deleted d-jack-knife

I have a dataset containing 45 observations. I want to sample times from this dataset, but with sample size equal to 35 each time. So each time I want to delete 10 datapoints from the original ...
1
vote
0answers
32 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
194 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
vote
1answer
56 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
176 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
votes
0answers
171 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
84 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 ...
-1
votes
1answer
1k 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
26 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 ...
2
votes
1answer
48 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
61 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
61 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
126 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
104 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?