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.

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Determining if dice are fair using statistics

A casino must demonstrate to the state gaming commission that every die it uses is fair. a machine is used to roll each die 1200 times. a die is discarded if the following assumption it is fair is rejected at the 10% significance level. determine if…
Stephanie Garibay
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Unconfounded assumption

In the notation of the unconfounded assumption, does $$\left(Y(0),Y(1)\right)\perp W \mid X $$ mean $$ f(Y(0),Y(1), W\mid X)=f(Y(0),Y(1)\mid X)\cdot f(W\mid X)$$ ? I can prove that the second line if the set of random variables $(Y(0),Y(1))$…
Ikuyasu
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Find $P(Y=5)$ for $Y=X_1+X_2+X_3$, where $X_i$ are mutually indpt Poisson R.V

In this problem, I am told that $X_1,X_2,X_3$ are mutually independent Poisson random variables with means $2,1,4$ respectively. I am also told to find the moment generating function for $Y=X_1+X_2+X_3$, which I found to be $M(t)=e^{7(e^t-1)}$. My…
An P.
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Chi-square table

I'm new to using chi-square table, and I assume that it should not be hard to use but yet I have some problems with it. I am due to find the following in a chi-square table: $P(Y>5)$ where $Y$ follows a chi-square distribution with $5$ degrees of…
slaiman
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Why prefer the t-score when the sample size is low?

According to this link: The general rule of thumb for when to use a t score is when your sample size meets the following two requirements: The sample size is below 30 The population standard deviation is unknown (estimated from your sample…
user1770201
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Paired Observation Hypothesis Testing

I'm doing a project presentation for applied statistics about hypothesis testing. Me and my partner claimed that the average amount of money that people spend per month on groceries is less than or equal to the average amount spent on dining out.…
Conrado Sanchez
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Sufficient sample size for 1 out of X sets

I want to create a "game" that aims at supporting the decision making. The user has to consecutively select one out of two random items. Each item belongs to one of X sets. My question is how many different choices are required to be sure which set…
Greeny
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Covariance of a random vector

If $Y_1,..Y_n$ are independent random variables, how do I work out cov$\begin{pmatrix}Y_1\\.\\.\\.\\Y_n \end{pmatrix}$? The covariance of the vector
usainlightning
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How to show some random variables are multivariate normal?

I've got several series of random data, which can be denoted as x1,x2,...,xn. How do I show that they are subjected to multivariate normal distribution? I refered to statistics textbooks but only got definations and properties. Do I have to estimate…
Liu
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Continuous Uniform Distribution Problem

Let $ X $ be a continuous random variable on the interval $ (a,b) $. The mean of $ X $ is $ 800 $ and the variance of $ X $ is $ 120,000 $. Calculate the range of $ (a,b) $. My default approach was to proceed as follows: $$ E(X) = \frac{(a+b)}{2} =…
cfairwea
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suppose a sample is taken from a symmetric distribution whose tails decrease more slowly than those of a normal distribution

I was wondering how to go about this question about Probability QQ Plots, the question is, suppose a sample is taken from a symmetric distribution whose tails decrease more slowly than those of a normal distribution. what would be the qualitative…
Yeti
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Formula for cumulative binomial probability

Is there a simple formula for finding a value of a cumulative binomial probability, eg. like the ones put in cumulative binomial probability tables? eg. X~B(50, 0.234) Find the cumulative binomial probability for 32, with one equation.
B.Jenkins
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Prove that the distance from the mean to the inflection points is one standard deviation.

Prove that the distance from the mean to the inflection points is one standard deviation. So I know in order to find critical points one must find the second derivative and set it equal to 0. However I'm confused how to approach this proof. Step by…
Lil
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To what extent can the measures of the properties of data sets restrict the possibility of what they can be?

Despite the trivial cases, such as 1,1 and 1,1,1, can there be two different sets of data that have the same central tendency and dispersion?
user321945
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Determining Sample Size for a Desired Margin of Error

I'm trying to study for a test in my AP Statistics course. My lecturer spent the majority of the unit going over the various proportion tests. On my review, I was presented with the following question: Suppose that you wanted to estimate p, the true…
Zulfe
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