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### Question

1. Let
η
,..., η
be n positive random variables (we do not assume their independence, in general). Prove that the distribution of η +...+ η is heavy-tailed if n1 n1 and only if the distribution of at least one of the summandsis heavy-tailed.
2. Suppose that ξ
,..., ξ
are independent random variables with a common n1
distribution F and that ξ
≤ ξ
≤...≤ ξ (1) (2) (n)
are the order statistics. (i) For k≤n, prove that the distribution of ξ
is heavy-tailed if and only if F is( k)
heavy-tailed. (ii) For k≤n−1, prove that the distribution of ξ − ξ
is heavy-tailed if and( k+1) (k)
only if F is heavy-tailed. (iii) Based on (ii) and on Probl 1 em , prove that ξ − ξ
has a heavy-tailed distri-( k) (l)
bution if and only if F is heavy-tailed.

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Q

### BMG880 Data Analytics and Business Intelligence

Task: AimsThe aim of this module is to provide students with the knowledge and practical skills for applying business intelligence and data analytics principles to support management decision making in a business context. The module also equips students' with quantitative analysis and data visual ...

Q

### HI6007 Statistics for Business Decisions

Question: Unit Learning Outcomes Assessed: Students are able to apply appropriate business research methodologies to support decision-making process. Students are able to identify and apply valid statistical techniques in a given scenario to solve business problems. Students are able to just ...

Q

### Management

Use google to find an example of a back to back histogram (or something like a back to back histogram, any thing that uses different histograms with the same scale to compare different groups) and discuss it , you have to find your own example that you understand, you cannot use the examples given o ...

Q

### ISTM 6214-Foundations of Artificial Intelligence

Assignment For this assignment, you will be working with the dataset Advertising.csv.  It consists of the advertising expenditure information of 200 companies as well as the sales data of these companies.  Build a linear regression model to examine the impact of advertising expenditure o ...

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