Questions tagged [arithmetic]

For on-topic questions involving arithmetic. Try to include also a more statistical tag. For purely mathematical questions about arithmetic, please use math SE https://math.stackexchange.com/

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40 views

Probability from Chi-Squared distribution

If I have a random variable called $A$ and $A \sim \mathcal{N}(0,1)$, how can I get the value of $X$ if $P(X<5A^2<6.52)=0.5310$. It seems that the answer is $2.4109$, but I don't know how to ...
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43 views

Equality of the Covariance of Two Random Variables and the Expected Value of the Product of One and the Difference Between the Other and Its Mean

I am trying to understand the second equality in the attached image. Could you please help me by guiding me as to how I can prove this? Thanks!
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1answer
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How can I normalize price history between -1 and 1 while keeping the ratio of price differences to each other the same?

I want to normalize a series of numbers to all be between -1 and 1, but I would like to do it in a way where the relative difference between price elements stays the same, if possible. Example list of ...
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Deep Learning: Should I dot product (input, weight) or dot(weight, input)? Does it even matters?

I've been following through Neural Networks from Scratch and found that the author switches the order of dot(input, weight) from time to time. The calculation shows that the dot product gives ...
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2answers
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How to calculate $\Delta Y$ given $\Delta X$, a simple linear equation, and a correlation score?

Suppose I conduct a correlation and SLR analysis on a bivariate data set and obtain the following: $$r=.63$$ $$Y=2.1+5.6X$$ If I increase X by 300, how much will Y go up?
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21 views

What is the expected value and variance of the arithmetic mean

How can I calculate the expected value and variance of the arithmetic mean? I know that is the arithmetic mean, but how do I use this to figure out the expected value?
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2answers
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Expected value homework question

Im not sure why the expected value that I got is incorrect. The method that I did is: (0)(0.568)+(7)(0.101)+(11)(0.218)+(9)(0.113)
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1answer
43 views

What mean should I use when few big values? [duplicate]

for a project I need to calculate several means, I then compare each of these means to a distribution under the null hypothesis H0. However sometimes some values (...
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1answer
36 views

Combine Two Numbers that Satisfies these Five(5) Conditions with R [closed]

I want two(2) numbers $\phi_{1}, \quad \phi_{2}$ such that the following five(5) conditions will be satisfied using R: $ \phi_{1} + \phi_{2} < 1 $ $ \phi_{1} - \...
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58 views

Odds to probability transformation

The odds are defined as $\omega = \frac{\pi}{1-\pi}$, where $\pi$ is the probability of some event. How can it be shown that the back-transformations is given via $\pi = \frac{\omega}{1 + \omega}$?
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25 views

Equation for weighted mean of percentages [closed]

I am trying to get the equation for a weighted average of percentages to be normalized between 0 and 1. Am I doing it correctly? Thank you so much!
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21 views

How to scale data proportionality as to equal 100%

I am applying for a grant for the nonprofit I run, and I have some data they need for the grant. However, this data does not equal to 100% and I need to know how to scale the data up so that it is ...
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1answer
319 views

Modelling exchange rates: how to log transform percentage changes?

I'm trying to model an exchange rate to test for extreme values. However, I have percentage changes from day to day. Given some changes are negative, I can't take the logarithm. Any idea how I could ...
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1answer
2k views

How to calculate 'times likely' for a percentage and whole number data set?

I'm analyzing speech data for single people vs those in group. I have two types of datasets for which I want to calculate "times likely". ...
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1answer
36 views

Finding the number of teams

I played in a online tournament of a game of some sorts, and I want to know how many teams they were. I have the following informations : The team who finished in first place were on the Top 0.001% ...
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1answer
362 views

Calculating variance of poisson distributed random variable

I am calculating variance of a Poisson distributed random variable with mean $\lambda$. I am doing it in the following way: $\mathbb{V}(X) = \mathbb{E}(X^2) - \lambda^2 \\ = \sum_{x\geq 0} \quad x^2\...
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1answer
91 views

Beta distribution, finding $\alpha, \beta$

Here the expected value and the variance are given, and it's needed to find the values of $\alpha,\beta$. From the Beta distribution and the elicited prior information, we can write: $E(\theta)={\...
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186 views

Negative variance of linear combination of regression coefficients

I'm going crazy over this so I hope someone can help me.. First a presentation of my case: I have a complex multiple regression model with 4 predictors (some terms that don't concern this issue are ...
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1answer
39 views

Simple Z-Score question dealing with normal mean and standard deviation I keep getting incorrect

The question below is simple, however, I got the question wrong despite following a basic formula I have been using for a while now. Here's the question: For applicants who actually entered medical ...
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1answer
28 views

Significance of Difference in arithmetic means

We characterized two social group through utilizing a 4 point likert scale and arithmetic means for 32 questions separated in 4 groups and 4 subgroups as our professor advised, we look at the ...
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0answers
190 views

Output Size of Mixture Density Networks

I am working on a neural network in which the final output layer will be a Mixture Density Network (MDN), but am confused about the shape of the values that final layer should return. In the paper in ...
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1answer
55 views

Squaring floats between -1 and 1 reduces sum of squares, so why do it? [duplicate]

I have been learning basic statistical testing as it relates to agriculture and have become familiar with the common practice of summing squared raw deviation values, whether in something simple like ...
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1answer
52 views

Question on finding the variance

]1 For part B, I previously had 2.07 which is incorrect but why?! I literally followed the formula and I encountered a similar problem on the internet that did the exact same thing I did done below: ...
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1answer
57 views

simply considering square root of Variance as Standard deviation

Consider the following simple linear regression equation: $$y_i=\beta_0+\beta_1 x_i+\epsilon_i,$$ where $\epsilon_i\sim N(0,\sigma^2)$. Suppose I have confidence interval of $\sigma$ which is (....
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0answers
56 views

Isn't HM a better way of averaging k fold cross validation scores than AM?

When calculating fscore we use the harmonic mean of precision and recall since hm penalizes situations when either of the two metrics is low while the other is large unlike the arithmetic mean. So ...
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1answer
23 views

Person months to annual risk

if a study reports a risk of 4 cases per 1000 person months can that be converted into an annual risk per 100,000 people? if so, how? Thanks
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1answer
191 views

Negative Binomial Coefficients -nCk = (n+k-1)Ck

I am unable to understand that why $\binom{-n}{k} = \binom{n+k-1}{k}.$ Please help me in understanding this.
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Brain teaser: 2 men can catch 2 fish in 2 minutes, at this rate, how many men can catch 500 fish in 500 minutes? [closed]

I found this interview question off of Quora. I'm unfamiliar with rate-related questions when there are 3 dimensions (men, fish, time). My intuition is: 2 men can catch 2 fish in 2 minutes then if ...
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1answer
48 views

Finding 'conditional probability'

Q-) The number of injury claims per month is modelled by a random variable N with: P(N=n)= 1/(n+1)(n+2),where n>=0 Determine the probability of at least 1 claim during a particular ...
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1answer
31 views

In Think Bayes book about Posterior mean

Page 24, Think Bayes by Allen B. Downey. Can you explain me how he compute mean by this code : ...
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1answer
31 views

Definition of nonarithmetic law

I came across the term nonarithmetic, but I don't now what that means. It is a condition for a Proposition of a Paper I am reading. There it is said: Assume that the law of $\ln A_0$ is nonarithmetic....
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1answer
62 views

Help regarding calculating z statistic and p value

I am trying to solve a problem but couldn't see any way around it. So far, here is the progress $\mu_{pop} = 10 $ $\sigma_{pop} = \sqrt12$ $\mu_{sample} = 12$ $z = (\mu_{sample} - \mu_{pop})/(\...
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26 views

Simplification of the Normal Kernel

The kernel of the normal distribution is typically written as : $ p(\theta | \mu, \sigma^2) \propto \exp\Big(- \dfrac{(\theta-\mu)^2}{2\sigma^2} \Big)$ where the normalizing constant is: $C = \dfrac{1}...
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1answer
403 views

Triangle inequality with random variables

Suppose $a$ and $b$ are real numbers (positive in my case), $X$ is a real-valued random variable and $F$ is a set of functions. Are the following true? $|a-b| \le E_X|a-X|+E_X|X-b|$ $|a-b| \le E_X [\...
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1answer
5k views

What is the underlying math needed to answer the following questions:

Some background: I was applying for an entry level business analyst position, and I was completely lost with some of these questions. These questions were from the practice test. I'm not sure how I ...
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1answer
498 views

Converting annual to daily mortality rate

In one excel workbook I am working on right now, the annual mortality rate is given as 3.082% And the formula for calculating the daily mortality rate is 1-EXP(LN(1-[annual mortality rate]/365) Why ...
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1answer
1k views

Is it better to take a mean of means or a grand mean when relaying rate data?

I am working with a dataset that includes number of fish caught in a day, and number of hours spent fishing that day. The variable of interest (outside of general summary statistics) is the number of ...
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0answers
110 views

How does this manipulation of summation of exponents work?

I found this paper by Fischer and Igel (2012) (1). I am not able to get past this last step in their derivations (eqn 22, p24) where $h_i$ are values of $h$. Can anyone tell me how they reduced the ...
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0answers
97 views

Non-linear regression model

Consider data consisting of pairs $(y_i, x_i)$ for $i = 1,..,n$ arising from a non-linear regression model: $y_i = \alpha + \beta\sin(\omega x_i + \delta) + \epsilon_i$ where $\epsilon_i \sim N(0,\...
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1answer
48 views

mean and least error on the line

Suppose I have a line on which i have points in non-decreasing order. My intuition tells me that if I want to minimize the squared mean error on some subset of 3 (or other number) points, I would like ...
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1answer
728 views

Geometric vs. Arithmetic mean to determine diameter of object

I want to estimate the volume of irregular objects (coral fragments) by simplifying their structure to a cylinder and then calculate the volume of this cylinder (i.e. Ecological Volume). The length ...
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47 views

Arithmetic and Geometric Means [duplicate]

The arithmetic and geometric averages provide a summary of historical performance. They are both unique in calculation and contain biases (as stated by my lecturer). My question is where exactly are ...
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2answers
323 views

plotting a factorial function in R

I have problem trying to plot the following function in R: The R code I'm using is: ...
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1answer
95 views

Comparing performance of 2 comparable tests

So I have sets of data, 15 responses for test A and 15 separate responses for test B. Tests A and B have 6 perception questions and the object is to compare the performance of representing data one ...
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4answers
5k views

Converting a Model from square feet to square meter

I have a simple regression fit for predicting house prices from square feet. The estimated intercept is -44850 and the estimated slope is 280.76 To make predictions for inputs in square meters, what ...
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1answer
71 views

How to write a fraction $\frac{n}{m}$ in the form $\frac{1}{x}$

If 663 million people don't have an item in the population of 7.3 billion, then 1 in how many people don't have it? What is the calculation I would use? How could I figure this problem for myself in ...
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2answers
6k views

Dividing or subtracting : Normal PDF's? of independent random variables [closed]

There is clear rule how to multiply OR sum Normal PDF's i.e. https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables $N_1(\mu_1,\sigma^2_1) + N_2(\mu_2,\sigma^2_2) = N(\mu_1+\mu_2,...
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825 views

Sufficient Statistic for inverse Gaussian Distribution

Let $X_1,...,X_n$ be a random sample from population with the pdf of the inverse Gaussian distribution $$f(x|\theta,\beta)=(\frac{\beta}{2 \pi x^3})^\frac{1}{2}e^{-\frac{\beta(x-\theta)^2}{2\...
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0answers
55 views

Correct term for negative difference between two values

A very newbie question! If the absolute difference between two values is the distance between them (and therefore always positive), what is the correct term for ...
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2answers
2k views

Difference between geometric and arithmetic mean

I still have problems to exactly understand the difference between geometric and arithmetic mean. I know that e.g. for returns, the arithmetic mean can be wrong (e.g. if I start with 100 $ and if my ...