# Questions tagged [means]

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.

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### Mean of means and standard deviation

I have a set of data with their means $\mu_1,\mu_2,\ldots\mu_n$ and standard deviations $\sigma_1,\sigma_2,\ldots,\sigma_n$. These values refer to repetitions of the same experiment. How do I ...
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### Urn problems: find mean and variance - stuck

I am stuck in a problem, and I can't think of a next step to find the solution. The question is the following: Suppose an urn has $k$ balls, numbered from $1$ to $k$, $k \in \mathbb{N}$. A sample ...
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### standard error of the difference in means

first off this my first post on here so if I missed out on a guideline tell me!! Okay so this is the problem I'm facing: I have 2 means of populations we want to compare. I also have the standard ...
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### Inequality harmonic and geometric mean

I'm trying to understand the proof on the bottom: https://artofproblemsolving.com/wiki/index.php/Root-Mean_Square-Arithmetic_Mean-Geometric_Mean-Harmonic_mean_Inequality He uses the AM-GM inequality ...
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### I was wondering about which mean I should use? The geometric mean or the arithmetic mean.

I have an optimization problem (minimization problem) and the table (below) represents a comparative study between the results of two methods, the first one performed better than the second one and to ...
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### should I use the mean or weighted mean in this example?

An investor calculated the percentages of each of three stock investments with payoffs as shown. Find the average payoff for the three stock investments. what should I use in this case to calculate ...
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### Finding variance without the data

A researcher is testing the effectiveness of a political video. She has randomly sampled 120 people to test the video. For each person, there is 50% chance the person will be Democrat and 50% chance ...
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### $Ε[Χ]$ calculations with different distribution variables

I have just started my stochastic processes course this semester and I came across this problem. I am missing something for sure because the $X_s$ confuses me. Let $A,B$ two independent random ...
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### Mean and Variance of total number of fishes.

The number of fishes caught by a skilled fisherman each day has a Poisson distribution with mean $2.5$. After $50$ days, what is the mean and variance for the total number of fishes the fisherman ...
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### Variance and mean of balls in bins limited capacity

Let there be $m$ indistinguishable balls, $k$ bins, $C$ capacity. Let $X_j$ denote the total balls in bin $j$. I've seen ways to calculate the total number of combinations, but I'm not sure how to go ...
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### Expected value of number of throws of a dice to get element $1$ four times

Here is the question: Find the expected value and variance of the number of times one must throw a dice until the element $1$ has been obtained $4$ times. My attempt: The minimum number of throws ...
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### How to calculate Measurement error of n measurements based on standard error and the quantile funcion

Let's say I have $n$ measurements $x$ sampled from a normal distribution X and I would like to estimate the mean with errors. Is the belove method correct? I'm mostly concerned about if I'm wording ...
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### MSE Minimized by Mean

In the Gaussian case, it is well-known that the MSE, is minimizer by the mean value. However, in general, if $X \in L^2(\mathcal{F};\mathbb{P})$, is a random-variable in $\mathbb{R}$, then is the ...
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### Is a definite integral just a summation?

I am learning about definite integrals and found the formula for finding an average of a function over a given interval: $$\frac{1}{b-a} \int_{a}^{b} f\left(x\right) dx$$ If we look at the average ...
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### What is the maximum value of $\frac{x^{100}}{1+x+x^2+\ldots+x^{200}}$?

If $x$ is positive, what is the maximum value of this expression: $$\frac{x^{100}}{1+x+x^2+\ldots+x^{200}}$$ This question is from a book of problems on sequence and series under the section on AM-...
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### Can a summation be transferred into the denominator?

I include a bit of an introduction, even though my main question is more mathematical. I was tasked with finding the Maximum Likelihood Estimate for $\theta$ in \mathrm P(X>x) = \left(\frac ax \...
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### How to show that the number of jobs is distributed equally

Sorry if I'm asking an obvious question. I have proposed a load balancing algorithm for a system of several devices. Suppose at first the number of tasks on each device is $device1 = 18$, $device2 = 8$...
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### Mean of the partial sum of the normalized Gaussian random vector

Let $X_1, X_2, \dots, X_d$ be $d$ independent $N(0, 1)$ random variables, and let $Y=\frac{1}{\|X\|}X$, where $X=(X_1, X_2, \dots, X_d)$. Let the vector $Z \in \mathbf{R}^{k}$ be the projection of $Y$ ...
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### Consider a random variable $X$ with the log-normal pdf $f(x) ={1\over \sqrt{2π}}x^{−1}exp^{{−0.5 (logx)^2}}$, $x>0$.

Consider a random variable $X$ with the log-normal pdf $f(x) ={1\over \sqrt{2π}}x^{−1}exp^{{−0.5 (logx)^2}}$, $x>0$. a) Find the mean and the variance of $X$. I know that $\int_0^\infty f(x) dx=1$...
### My goal is to calculate $\operatorname{Cov}(X,Y)$, but I'm struggling to calculate $E[XY]$
Regarding the following problem: A fair coin is tossed 5 times. Let $X$ be the number of heads in all $5$ tosses, and $Y$ be the number of heads in the first $4$ tosses. What is \$\operatorname{Cov}(...