# 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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### Calculate conditional probability using mean and variance

I have a set where its values follow a normal distribution, but I only have the sum of all of them, and the sum of its squares. Having: $\sum_{i=0}^n X_i$ and $\sum_{i=0}^n X_i^2$. I have the ...
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### Correlation of means or correlation of individual values

I have a data set of player performances and am looking to calculate some correlations of their stats with win percentage. Some players have multiple performances, is it valid for me to take the mean ...
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### I can't think how to approach this statistics problem?

A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data? ...
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### Mean and Median are equal. Find x and Y. X and Y are natural numbers. [closed]

4,6,x,y,10. The mean and median are equal to each other. Find x and y?
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### Hypothesis testing for sample means within a normal distrubution

The context of the question is that a bakery bakes cakes and the mass of cake is demoted by $X$ such that $X \sim N(300, 40^2)$. A sample of 12 cakes is taken and the mean of the sample is 292g. The ...
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### Calculating the Mean of a Range with Floor and Ceiling Functions?

I did a survey a couple months back, and one of the questions required a range of numbers. I may have discovered my own formula for how to calculate the mean of a range of numbers, but I don't know ...
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### Limit of generalized mean with exponent tend to zero

How to get the following limit: $$\lim_{p \to 0}\sqrt[p]{\frac{1}{n}\sum_{i=1}^{n}x_i^p}=\sqrt[n]{\prod_{i=1}^n x_i}$$ I.e. how to get geometric mean from definition of generalized means? I attempted ...
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### Compute the correlation coefficient $r(X_{(1)},X_{(3)})$ .

I got this problem where: The random variables $X_1, X_2,$ and $X_3$ are independent and $Exp(1)-$ distributed. Compute the correlation coefficient $r(X_{(1)},X_{(3)})$ . I know through research ...
I encountered this inequality when reading some paper, however, why it holds does not seem very obvious to me: Consider nonnegative real numbers $a_1, ..., a_n, b_1, ..., b_n$, and $b_i \leq \frac{... 2answers 73 views ### Variance and mean of balls in bins limited capacity Let there be$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 ... 2answers 42 views ### 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 ... 0answers 16 views ### 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 ... 0answers 16 views ### 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 ... 3answers 575 views ### 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-... 1answer 63 views ### 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 $$\mathrm P(X>x) = \left(\frac ax \... 4answers 2k views ### Is a definite integral just a summation? I am learning about definite integrals and found the formula for finding an average of a function over a given interval:$$\frac{1}{b-a} \int_{a}^{b} f\left(x\right) dx$$If we look at the average ... 0answers 19 views ### 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... 1answer 19 views ### 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 ... 1answer 38 views ### 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... 1answer 29 views ### Is there a formula for the silver spiral? I can construct a golden spiral by rotating segments 90 degrees and scaling their segments by the golden ratio, and then use the polar formula on wikipedia to interpolate points at other angles to ... 2answers 36 views ### 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}(... 1answer 45 views ### Computing the overall mean value in a game of chance with related means Suppose you are presented with the following game: Game Interface How the game works: Player places bets on one or more symbols. The wheel is spun. If the wheel lands on a symbol that the player ... 1answer 21 views ### How should I calculate mean CI - from raw data or mean values? I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ... 0answers 16 views ### Is there an upper bound for the mean of a ratio between two random variables? Is there an upper bound for the mean of a ratio between two random variables ? 0answers 10 views ### Standardising a score of values I am working on developing on a standardised score from a number of scores. The values will be ranging from large to small of each score and I am trying to develop a way of proportionally measuring ... 0answers 18 views ### Best Average to Represent Quantitative Data? For a final assignment, my two group members and I have created a biased survey called Should Public Schools Implement a Uniform Policy? We have about 2-3 ... 0answers 19 views ### Do two pairs of distinct natural numbers exist such that AGM(A,B) equal to AGM(C,D)? Here AGM is arithmetic-geometric mean. Are there natural numbers A,B,C,D such that 1\leq A<C<D<B and arithmetic-geometric mean AGM(A,B)=AGM(C,D) ? In other words, is AGM a homomorphism ... 0answers 22 views ### Can arithmetic-geometric mean of two distinct natural numbers be a natural number? Are there solutions to equation AGM(A,B)=C such that 1\leq A<B and A,B,C\in\mathbb{N}? 1answer 43 views ### Mean vector and covariance matrix I am given a home work for one subject, but my probability theory course is just started, so I dont have enough information. Could someone help me with that? Given:$$\begin{equation} p_\underline x(... 0answers 61 views ### Sampling uncertainty (uncertainty in standard deviation) Say I took twenty measurements of the wind velocity at a point. This is a sample of the infinite number of measurements I would need to get the true velocity at that point. I then calculate the mean ... 3answers 2k views ### What is the mathematical meaning of this question?$a,b,c \in\mathbb{Z}$and$x\in\mathbb{R}$, then the following expression is always true: $$(x-a)(x-6)+3=(x+b)(x+c)$$ Find the sum of all possible values of$b$. A)$-8$B)$-12$... 1answer 44 views ### Range of Data Values That Includes 95% of my Data For a math assignment, I am required to find the range of data values that would include 95% of my data. My data is the wait time for a specific bus. I have gathered 20 pieces of data for this, ... 1answer 82 views ### Generalized AM-GM Inequality I was discussing means with my friend, and I tried to illustrate the concept of geometric mean using the following idea: Suppose we have two positive quantities$x,y>0$. The simplest geometric ... 0answers 34 views ### Statistical problem: Scores, Weights and Averages As part of a software development project, I'm trying to find the correct mathematical approach for a statistics problem involving scores, weights and averages. Here's a simplified summary of the ... 0answers 12 views ### Hypothesis Testing for Probability and Statistics Question: The present defective rate of a product in a certain factory is 3%. A random sample of 250 of products produced using a new technique which is supposed to improve the quality of production ... 0answers 49 views ### Generalized definition of all means of$n\$ numbers?
What are the questions that are asked whose answer yields the geometric and harmonic means. For example, we arrive at the arithmetic mean by solving: $$\min_y \sum_{x \in S} (x - y)^2$$ What ...