Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
1
vote
1 answer

How "normalize" with a min value while keeping the weights?

I have a list of positive numbers given. By dividing each element by the sum of all elements, I receive a normalized result between 0 and 1 while keep the weights: before [12, 12, 0, 0, 0] -> after [12/24, 12/24, 0, 0, 0] = [0.5, 0.5, 0, 0,…
TeaCup
  • 113
1
vote
1 answer

How does the mean of the square of differences make everything positive?

In a Deep Learning lession, the author explains that 2 black / white images can NOT be compared by looking at their pixel value differences because some values would be negative, and they would cancel each other out. For example: pixel (0,0) of…
tmighty
  • 393
1
vote
1 answer

What are the range and mode of the set {5}?

What is the range of the set {5}? Is it zero? What about its mode? Is it 5? This is taken from a GRE question. My reasoning is as follows: 1) The range is the highest value minus the lowest value, and since there is only one value, it should be…
Joebevo
  • 1,439
1
vote
1 answer

Is the likelihood a function of random variables ($X_i$) or a function of realisations of random variables ($x_i$)?

Is the likelihood a function of random variables ($X_i$) or a function of realisations of random variables ($x_i$) ? Is there a consensus on this in the statistics community ?
Mathieu Krisztian
  • 240
1
vote
1 answer

Are there two formulas under the null hypothesis for the test statistics of the comparison of proportions of two samples?

When comparing two proportions of two independant samples of size $n_A$ and $n_B$ (with random variables $X_A^i$ and $X_B^i$ following a Bernoulli law $B(p_A)$ and $B(p_B)$) using a test statistics, and dealing with the null hypothesis $H_0$ that…
Mathieu Krisztian
  • 240
1
vote
2 answers

What is the difference between a two sample t-test and a paired t-test?

I have the following question from AP statistics: Two friends were curious if it was faster to use the drive-thru or order at the counter at their favorite fast food restaurant. For 555 different visits, one of them ordered at the counter while the…
Sahil
  • 179
1
vote
1 answer

How to find out which distribution(sample) a number is coming from?

Suppose I have two data samples of the same size N generated from two separate distributions, and a new number is given. How could I find out which distribution this new number is coming from? What should I do if the sample size were different? My…
www
  • 43
1
vote
1 answer

MoM of Uniform Distribution

I'm trying to learn MoM. I'd like to find MoM and show $\hat z_{MoM} $ is unbiased for $U(- \sqrt z, \sqrt z)$, which has a density function: $f(x,z)= \begin{cases} \frac{1}{2\sqrt z} & -\sqrt z \leq x \leq \sqrt z \\ 0 & otherwise …
RChamuel
  • 31
1
vote
1 answer

Random sample as random variables?

Suppose we perform a random experiment. Let us write $\Omega$ for the respective sample space. I'm trying to make sense of a sample of size $n$. Should it be: (1) A sequence of random variables $X_1, \ldots, X_n: \Omega\rightarrow \mathbb R$? or (2)…
PtF
  • 9,655
1
vote
1 answer

Do residuals vs fitted plot have to be concentrated around the x-axis?

Since the residuals and the fitted values are independent, we would expect the residuals to be distributed evenly around some horizontal line, if the model is linear. But does this horizontal line have to be the x-axis? I think in the cases when the…
XXX
  • 409
1
vote
1 answer

Evaluate the following for a standard normal probability distribution, drawing an appropriate picture ...

Evaluate the following for a standard normal probability distribution, drawing an appropriate picture. A.) Find the standard normal z-value so that the area that lies to the right of z is 0.2119. For part A, I did P(Z > 0.8) = 1 - P(Z < 0.8) =…
user102156
  • 445
1
vote
1 answer

Find the following probabilities for a standard normal distribution $P(|Z| > 2.05)$

I have $P(|Z| > 2.05)$ $P(-2.05 < Z < 2.05)$ $P(Z < 2.05) - P(Z < -2.05)$ $0.9798 - 0.0202$ and got my answer to be $0.9596$ but it seems off. I do not know where I missed a step. Any help would be much appreciated.
user102156
  • 445
1
vote
1 answer

Calculating the minimum size of a sample

A company has 2.400 employees. You want to extract a sample of employees to test the quality of the food of the refectory. On a pilot sample, in a scale of 1 to 10, the satisfaction degree grades got a mean of $6.5$ and a SD of $.2.0$ a) Calculate…
Akari Oozora
  • 287
1
vote
1 answer

How do I draw a roc (receiver operating characteristic) curve

Suppose I want to build a model to predict if someone has a certain disease. 1 means they have the disease, 0 means they don't. From what I've read, my model's output domain is all real numbers. So my model's output might be Patient Number, Model…
Ben
  • 369
1
vote
0 answers

Is $(\mathbb{R},\mathcal{R},\{N(\mu,1): \mu \in \mathbb{R}\})$ a complete statistical structure?

Let $B \in \mathcal{R}$ and $N(\mu,1)(B)$ a free event, wich means it doesn't depends on the unknown parameter $\mu$. Then prove that $B$ or $B^c$ is $N(\mu,1)$-null. I've alredy proven that if the statistic structure is complete, then the only free…
Milamaranth
  • 83
1 2 3
…
99 100