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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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How should graphs of True Positive Rate / False Positive Rate be interpreted?

I have recently seen some graphs like this in the context of classificaiton: Source: http://on-demand.gputechconf.com/gtc/2014/webinar/gtc-express-convolutional-networks-webinar.pdf, page 85 How should one interpret these graphs? My try In this…
Martin Thoma
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How to conceptualize and calculate the variance in the waiting time?

I'm trying to calculate the mean and variance in the waiting time for the following situation: You are at the grocery store waiting to check out. There are 100 people in the line, and 10 cashiers. Each person takes on average 'n' minutes, with a…
Angband Addict
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Applications of the binomial distribution and its approximation by Normal or Gaussian PDFs

any one to help me with descriptions or to tell me where i can retrieve the answers for this kind of question. Describe in detail the circumstances in which the binomial distribution can be applied,and when can it be approximated by the normal or…
Junior II
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Deduce that $\mathbb E(X^3)=1^3+2^3+3^3+4^3+5^3+6^3$

A fair die is tossed and let the random variable $X$ be the number that appears. Deduce that $$ \mathbb E(X^3)=\frac{1^3+2^3+3^3+4^3+5^3+6^3}6. $$ First of all, I would like to know the probability distribution of this random variable $X$.
Junior II
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Shortest Confidence interval for $\beta^2$

let $x_1,x_2, \ldots, x_n$ be a random sample from distribution under function distribution: $$F(x)= \left( \frac{x}{\theta} \right)^\beta, \quad 0 \leq x \lt \theta.$$ Where $β$ is unknown but $θ$ is known. find a shortest confidence interval in…
saeedhamidi
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Given a set of numbers, how to determine if variable x is significantly "in the middle" of the set?

I am working on an electronics project which requires some statistical analysis and I'm forgetting how to work this out. I have a compass which determines (x,y) magnetic pull. The problem is that the compass will return multiple values without…
binarylegit
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Find expected value and variance from pmf.

I have a question about pmf: The n candidates for a job have been ranked 1, 2, ..., n. Let X be the rank of a randomly selected candidate, so that X has pdf has pmf p(x) = 1/n if x=1,...,n & 0 if otherwise. Compute E(X) and V(X). I know the E(X)…
Keris
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Delta Method and Consistency of Estimator

Let the random variable $y_1$, $y_2$, ..., $y_n$ be iid Poisson($\lambda$). Let $g(\lambda)=\sqrt {\lambda}$, and let $\hat{\lambda} = \overline y$. (a) Use the Delta Method to find $E(\hat{\lambda} )$ and $Var(\hat{\lambda})$. (b) Argue that…
Brian
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Probability Question Finding Salary

The population mean annual salary for environmental complicance specialists is about \$60,000. A random sample of 35 specialists is drawn from this population. How would I find the probability that the mean salary of the sample is less than…
math
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venn diagrams - How can this event be shown?

I have this venn diagram For which i have shade (A ∩ B ) ∪ C. I see where A and B intersect, but i don't how a union should appear between the intersection and C. Could someone clarify where i am going wrong?
stats
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What are the chances of a sample distribution, given that I know the larger population's distribution?

I know that the larger population, of size m, follows a normal distribution. I have some sample that is size n, and follows its own particular distribution, which is not normal. Given my sample sizes, what are the chances that I would get the…
orange1
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Median of grouped data

part (ii) Median = $Lm +(n/2-cf)/fm*h$ = $171+(20-16)/12*3$ = $172$ am i correct?
user2463158
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Why the standard deviation approximated by the range rule of thumb much different from the standard deviation calculated directly from sample data?

What makes the standard deviation approximated by the range rule of thumb much different from the standard deviation calculated directly from sample data? For example, if the approximate standard deviation is 15.36 and the standard deviation…
Guess
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Calculating expectation and using the delta method

Let $\hat{p}$ be the proportion of successes in $n$ independent Bernoulli trials each having probability $p$ of success. (a) Compute the expectation of $\hat{p} (1-\hat{p})$. Isn't $P(\hat{p} = k) = \binom{n}{k} p^k(1-p)^{n-k}$? So is…
symmetricuser
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Problem about exponential MGF

I have a question: $X$ is an exponential random variable with mean = 5. Let $Y=2X+3$. I'm required to find $M_Y(t)$, the moment generating function of $Y$. Well I used the property that $$M_Y(t)=M_{2X+3}(t)=M_X(2t)\cdot M_3(t)=e^{3t}\cdot…
jojo
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