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
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What does it mean to raise a distribution to a power?

What does it mean in statistics if we raise distributions to the powers? Like if $X$ is uniformly distributed on $[0,1]$ then what is the distribution of $X^3$ or the expected value of $X^3$?
guest
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Statistical tests for checking that the mean is less than some value and for comparing two population means

How do I do a statistics test that my population mean is less than some value (rather than equal to some value)? I want to do this in two flavors: sample 30 oranges and test whether the average weight of an orange from my population is less than 1…
Alex Reece
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Finding the p.d.f. of T=XY using the C.D.F. Technique (Functions of Random Variable)

Suppose X and Y are continuous r.v. with join p.d.f. $$f(x,y)=3y, 0 \le x \le y \le 1$$ Find the p.d.f. of $T=xy$ So I know that we can consider for $ t < 0, P(T \le t)=0$ and if $t \ge 1, P(T \le t)=1$ Therefore we consider $t \in (0,1)$. But I…
HC1994
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Using distribution properties to find the exact value of the following sum

$\sum_{x=1}^\infty \frac{x^2}{2^x}$ I believe I should be using geometric properties. So I'm trying to get it to resemble $\sum_{x=1}^\infty xp(1-p)^{x-1}$ But I can't seem to manipulate it how I'd like. Am I incorrect in assuming it's closest to a…
fossdeep
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Proving induction on a binomial distribution

I have to show that $p(k+1) = \frac{n-k}{k+1}p(k)$ So far, I have done some manipulation. $p(k+1) = {n \choose k+1}p^{k+1}(1-p)^{n-(k+1)}$ $p(k+1) = \frac{n!}{(k+1)!(n-(k+1))!}p^{k+1}(1-p)^{n-(k+1)}$ $p(k+1) =…
fossdeep
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Determine Marginal Probability density function of X

Random Variables X and Y have the joint probability density function f(x,y)= 8xy/81 for 0 < x < 3 and 0 < y < x Determine the marginal probability density function of X. I am confused if I should be using integration of 0 to X or 0 to…
Brian
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Finding probability $P(x + y \le 1)$ given the joint pdf

So in the problem I was given the joint pdf $f(x,y) = x + y$, $0< x <1$, $0< y <1$, $0$ elsewhere. I am tasked to find $P( x+y \le 1 )$. My intuition was to $\int_0^1\int_{1-x}^1 (x+y) \, dy \, dx $ working that out, i got the answer of 50%. Is my…
user3388780
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Basic statistics: outliers, mean, median

For a sample of data, I got that the mean = 4.31 and the median = 4.42. Also, 36% of the values from the sample are less than the mean. Does this illustrate that the data is skewed left?
Will
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Proof Chebyshev's Inequality

I want to proof Chebyshev's Inequality using Markov's inequality. Cheb.Ineq: $$P(|X-\mu| \ge a) \le \frac{Var(X)}{a}$$ So I'm starting with Markov's Inequality: $$P(|X-\mu| \ge a) \le \frac{E(|X-\mu|)}{a}$$ I replace $|X-\mu|$ by $(X-\mu)$, and…
Peanut
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Find all possible numbers with specific mean, median and range

Given that there are $20$ positive numbers and that the median is $42$, mean is $46$ and the range is $35$. An important condition, I missed: A number can appear at the most two times. This was indeed question asked in my sister's class (6th grade).…
Siddhi V Iyer
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Small question concerning the proof of the unbiased estimate of the population variance

The main purpose of this question is to check my understanding. As in I have an answer that I think is correct, but I'm not sure, since Stats is not my forte. So given a random variable $X$, we take some samples from it and denote by $X_i$ the…
Diana
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Regression of Irregular Exponential

I am trying to model the population growth of countries with the following logistic equation: $$p(t) = \frac{P_oK}{P_0+(K-P_0)e^{(-rt)}}\tag{displayed}$$ Where $p$ = population; $P_0$ = initial population; $K$ = carrying capacity; $r$ = constant;…
Mr. Scarecrow Jack
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Example questions for bias/consistent estimators.

Now, I know how to do this particular one, but I was wondering if anyone had a place to get questions similar to this? I've tried googling, but have not come up with anything. Consider the regression model: $y=Bx + u$, where $\mathbb{E}(u)=0$,…
pbdemons
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Degree of freedom in statistic

I am always having difficulty understanding what degree of freedom really is. I know that when I post this question people are going to tell me to do some research myself but I did it and I am still having problem understanding it. I watched youtube…
Ryan Kung
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How to make statistical sense of this experiment:

I have conducted an experiment but I am now unsure of how to say, from a statistics point of view, that the data supports or not that a certain phenomenon has occurred, meaning it could be mere measurement error. This was the experiment: a sample of…
aristotle85
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