# Questions tagged [mean]

The expected value of a random variable; or a location measure for a sample.

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### Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
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### $\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$, upper bound second moment from first moment

Let $X$ be a non-negative random variable bounded on $[0,1]$. Is it true that $\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$ for some constant $k$? If not, are there any minimal assumptions on $X$ where this ...
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### Conditional and unconditional mean in GARCH(1,1) model

Say I have a stationary time series and want to fit a GARCH(1,1) model. Does this mean that the conditional mean, which is used in GARCH, would always be the same as the unconditional mean of the ...
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### Sample mean of subsample appended to original sample [closed]

From an $SRSWOR(n)$ drawn from $N$ units, an $SRSWOR(n_1)$ sub-sample is drawn and added to the original sample. Show that the sample mean based on $(n + n_1)$ units is an unbiased estimator of the ...
1 vote
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### Can raw means and estimated marginal means be the same ? And when?

I have read a lot about calculating raw (standard) means and EMM. First are data based (descriptive stats), the latter are model based. I try to learn how to calculate both of them. In my example both ...
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### Why is taking the mean RMSE sometimes so far off overall RMSE?

I'm working with a multi-threaded program, which splits a dataset into N chunks, and evaluates some regression model's performance, predicting a score for each item in each chunk. I'm using RMSD as ...
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### compare means of lognormal distribution

I have a small set of data that I used to generated a lognormal distribution: ...
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### Can I compare two estimates by their sample variance?

For example, to estimate the population mean $\mu$, I am given two sample mean $\bar{x}_1$ and $\bar{x}_2$ from two (independent) data sets of $N_1$ and $N_2$ observations respectively. Without access ...
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### Confirming my calculation of mean, standard deviation and median for a histogram

Average travel time* for men = 27.2 minutes, women = 23.6 minutes My calculations are the followings: The problem is my calculated mean is 28.4 but chart says 27.2 I calculate the mean with this ...
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### Can ANOVAs or Student tests be conducted on any summary statistic at the individual level?

I am wondering if ANOVAs or Student tests can be performed on any summary statistic of performance at the individual level without any effect on type 1 and type 2 error. For example, consider a simple ...
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### How does a Random Sample relate to Random Processes and Random Variables?

What is the difference between a Random Sample, Random Variable (RV) and Random Process (RP)? As far as I know, a RV is a mapping from an experimental space to the real numbers and a RP is a mapping ...
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### Comparing ratios of independent means by calculating SE difference – applicable?

I am conducting a study comparing the ratio of a mean number of vocalizations to the mean number of individuals across three treatments. For each treatment, I have the mean number of vocalizations (...
1 vote
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### General Expression for the $t$-th difference of conditional means

In econometrics, it is common to work with the difference-in-differences of conditional means. For example, let $Y$ denote a variable of interest and $X_{1}$ and $X_{2}$ denote binary regressors. The ...
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### What do I do when I *want* to accept the usual null hypothesis?

I have samples from two random variables, and I'm assuming normal distribution with equal variance. I want to show that the distributions have equal means $\mu_1$ and $\mu_2$. The usual two-tailed t-...
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### Why is this derivation of the mean of the gamma distribution using the log-partition function incorrect?

I am using this formulation of the exponential family : $$\large f_{X}(x;\boldsymbol{\eta})=h(x) \exp \left(\boldsymbol{\eta} \cdot \mathbf{T}(x)-A(\boldsymbol{\eta})\right)$$ The gamma distribution ...
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### Why is E(θ / (1 - θ)) different than E(θ) / (1 - E(θ))?

I've encountered a problem question: The probability of success for a random variable follows a Beta(5, 3) distribution. The posterior mean is θ = 0.625. The odds of success is defined as θ / (1 - θ)....
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### How to aggregate standard errors of multiple test scores?

I have three test scores of a student. The three single scores are generated by an IRT-based test using computer adaptive testing and are reportet with standard error bars. For the report I want to ...
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### Can you create an age structure of population, if the age was established using multiple different methods?

I want to analyse a age structure of my sample. However, I was not given the ages themselves and instead had to establish them using multiple methods with various coefficients of determination (not ...
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### Standard deviation squared is variance. What is standard error of the mean squared? [closed]

Is it correct to say that there is a sample variance and a mean variance, and their square roots are the standard deviation and the standard error of the mean, respectively?
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### Versatility and validity of aggregate algorithm for a multiple criteria decision problem (averaging)

I'm trying to aggregate different variables in multiple scales and distributions. The distributions are not known beforehand, but I want to generate a general statistical value that represents all the ...
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### Optimality criterion for mean estimators

Assume a sample size of $n>5$, a given variance $\sigma^2 > 0$ and a $\delta \in (2e^{-n/4}, 1/2)$. Proof that there exists a distribution with variance $\sigma^2$ such that for any mean ...