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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.

3 votes

Strange distribution of movie ratings

It is a case of a Bimodal Distribution which will have two Peaks. In general , these Bimodal Distributions are a "mixtures" of 2 Unimodal Distributions , which may be hidden. Here , I would guess (bec …
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1 vote
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Percentage of values between 3 standard deviations and 4 standard deviations.

According to https://blog.masterofproject.com/six-sigma-statistics/ : $\pm 1 \sigma : 68\%$ $\pm 2 \sigma : 95\%$ $\pm 3 \sigma : 99.73\%$ $\pm 4 \sigma : 99.9937\%$ $\pm 5 \sigma : 99.99994\%$ $\pm 6 …
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1 vote

How certain distributions can be treated as normal distribution?

Practical "target output" Cases like Electrical Engineering & Chemistry & Machine Learning & Statistics might make do with $3.14159$ Like-wise : When we have a large Data-Set & want to analyze it , we …
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1 vote

Can the Monte Carlo method be used to determine whether an integral exists?

I think the Answer is Negative. When the Integral is converging , we might use random Points on the Curve to "estimate" the value & make some way to quantify the "accuracy". When the Integral is not c …
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1 vote

6 possible options on each of 3 days. How many arrangements are possible? (Is this as terrib...

[[1 ]] Lack of Clarity : Well , YES , the Question could be written with a little more clarity , since it can be taken in various ways. [[ 2 ]] "Am I missing something that makes the first interpretat …
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3 votes
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Comparing the dissimilarity of the order of integer sequences

There are various (Dis)Similarity measures. (A) You have given Dot Product , which is very common. $S=\Sigma a_ib_i$ (B) Commenter Malady has indicated Vector Norm , though there are variations there. …
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1 vote

What is the conceptual misunderstanding in the hat-check problem (derangements)?

Consider this Image , where the upper line has the letters $l_1,l2,\cdots,l_n$ & the lower line has the Envelopes $E_1,E_2,\cdots,E_n$ , where I have taken Example $n=5$. The Grey Dotted lines will Co …
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0 votes
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The Collector’s Problem

Your way is not right. It will under-count & over-count certain Cases. Let $n=8$ & $r=5$. You want to put the $5$ in some order , then rest $3$ you want to put in-between those $5$. Issue 1 : you are …
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