# 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 Value and Variance of a Birth and Death Process

Let $\{X(t)\}_{t>0}$ on $\{0,1,2,3\}$ a birth and death process, with $\lambda(s)=(3-s)^2$ and $\mu(s)=s^2+s$. Assume $P(X(0)=3)=1$ and determine: (a)$E[X(t)]$; (b)$Var[X(t)]$. I don't know how ...
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### Does this three number mean have a name? (Carlson elliptic integrals)

Recently I found out about Carlson elliptic integrals, which have great symmetry properties and allow to compute every kind of elliptic integrals and other functions. The question is about the method ...
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### how to subtract mean from a set of SPD matrices

I have a set of SPD matrices and I know how to calculate their mean. My question is: Is there any method to subtract the mean from each sample? In Euclidean space we simply subtract the mean from ...
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### Limit superior and inferior of Cesàro means

From a sequence $a^x_n$, define the sequence of its Cesàro means $a^{x+1}_n$ as $$\sum_{k=1}^{n} a^x_k/n$$ It is easy to show that the sequence of Cesàro means of a bounded sequence will itself be ...
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### Is the mean of the Weierstrass function defined?

The Weierstrass function is an example of a function that is continuous everywhere but differentiable nowhere. My question is whether the mean $\bar{f}$ of the Weierstrass function $f(x)$ can be ...
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### game with 3 dice - profit of player

A player rolls 3 dice (6 sides) simultanuously. If at least one 5 or 6 appeared he wins 2 dollars. In any other case he loses 6 dollars. a) Find pdf of random variable $Y$ profit of player at a game b)...
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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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### Finding new mean and standard deviation given initial values for both

I'd appreciate any assistance on this: On average, a salesperson makes a sale to 60% of their contacts in a given day with a standard deviation of 2.2%. Assume the salesperson makes 20 contacts per ...
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### Generalized Mean Inequality with STD

I am looking for a formal proof shows that for any $x\&y \geq 0$ and $\alpha > 1$, $$\frac{1}{n}\sum_{i=1}^{n}x_i ^\alpha \geq \frac{1}{n}\sum_{i=1}^{n}y_i ^\alpha$$...
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### Mean and correlation of product of two random processes

I have two random process: $$A(at)$$ $$cos(2\pi f_0t+\Phi)$$ with these hypothesis: $a$ and $f_0$ are constant $\Phi$ is uniformly distributed in $[0,\pi)$ $A(at)$ is WSS I must calculate the ...
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### Partitioning an equation into summable components

For this actual issue I think the physical setup can most easily be thought of as a tray upon which a set of non-overlapping colored disks are randomly placed. All disks of the same color have the ...
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### Poisson and Negative Binomial distributions- Mean and Variance total claim size

I am trying to do the following: Let $S$ be the total claim size when the number of claims follow a Negative Binomial Distribution. How can I derive a formula for the $E(S)$ - expectancy and $V(S)$ -...
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### Mean of minimum of an inverse Rician random variable

What is $E\left[\min\left(\frac{1}{X}\right)\right]=?$, where $X$ is a Rician distributed random variable. I know from this article that the first moment of an inverse Rician distributed random ...
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### Nice mean for negative Numbers

I'm searching for a nice mean (or average) for negative numbers that gives less weight to high (absolut) outliers (I don't have enough values to use median). Obviously the way to go for positive ...
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### how to estimate weight for weighted product?

I know that one way to estimate the weighted sum method is to use the inverse of each attribute's variance: $1/\sigma^2$. In wiki, it is saying: The significance of this choice is that this weighted ...
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### Representing gaussian variables by real scalars

Sometimes we may need to do qualitative analysis of multiple Gaussian variables $\mathcal{N}(\mu_1,\sigma_1^2),\mathcal{N}(\mu_2,\sigma_2^2),\ldots$. A naive strategy would be to just compare their ...
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### Deriving confidence intervals for a random variable that is not observed directly (example)

So I have a question about combining random variables. While it is given that a bottle filling machine fills with $\sigma=5$, the observed variable here is the weight of $n$ bottles, where the bottle ...
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### Probability problem - Standard Deviation related

Exercise : A car insurance company has $10.000$ customers. The average annual compensation per customer is $240$ with Standard Deviation $800$. Calculate by approximation the probability of the total ...
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### Estimate the median from mean, variance etc.

I'm given four groups containing 15 observations each. I can only see a few of the observations. However, for each group, I'm given the variance, mean, sum, USS, SSD etc. I have to estimate the ...
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### Variance of the gain, given a set of wagers on $n$ Bernoulli trials

Let's assume we want to wager on a given set of n Bernoulli trials with probabilities $p_i$ with $i \in \{1, 2, ..., n\}$ and a corresponding payoff odds $b_i$, i.e., betting a certain percentage \$f_i ...
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### Geometric mean of prime twin gaps?

This question is an analogue of Geometric mean of prime gaps? Where primes have been replaced by prime twins. Eric's answer : In 1976 Gallagher proved, under the assumption of a uniform version of ...