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### Question

Competency 2: Describe the concepts, processes, and tools required to conduct comprehensive health assessments for individuals, families, communities, and populations.
Describe the data necessary to make an informed community health assessment.
Explain how data helps determine the health care needs of a community.
Describe a strategy for obtaining data needed for a community health assessment.
o    Explain how to establish the validity and reliability of data used in a community health assessment.
•    Competency 3: Explain the internal and external factors that can affect the health of individuals, families, communities, and populations.
o    Explain the factors that affect the health and wellness of a community.
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.Prove the Cauchy distribution is subexponential and strong subexponential. 3.2.UsingdirectestimatesforconvolutionoftheParetodensity,showthePareto distribution is subexponential and strong subexponential. 3.3. Using direct estimates for convolutions, prove that any regularly varying at inï¬nity distribution is subexponential and strong subexponential. 3.4.LetF andGbetwodistributionsthatareregularlyvaryingatinï¬nity,andlet 0 < p < 1. (i) Prove that the distribution pF +(1−p)G is regularly varying at inï¬nity. (ii) Prove that the distribution F∗G is regularly varying at inï¬nity. 3.5. Prove by direct calculations of convolution density that the exponential distribution is not subexponential. 3.6.Supposethatξ ,...,ξ areindependentrandomvariableswithcommondis1 n tributionF.Provethemaximum,max(ξ ,...,ξ ),hassubexponentialdistributionif 1 n and only if F is subexponential. +3.7. Suppose that F and G are weakly tail-equivalent distributions on R . Prove thattheconvolutionsF∗F andG∗Gareweaklytail-equivalenttoo.Provethesame for n-fold convolutions, for any n≥3. 3.8. Suppose that ξ , ..., ξ are independent random variables with a common 1 n α1exponential distribution. Find the asymptotics for probability P{ξ +...+ξ > αn n1 x}as x→∞if (i) allα > 1; i (ii) allα < 0; i (iii) allα 6∈[0,1]. i 3.9. Let non-negative random variable ξ have the Weibull distribution with the β− xtail F(x)=e ,β >0.Forwhichvaluesofα >0,doesP{ξ+ξ >x}∼P{ξ >x} α  as x→∞? 1−α α αHint: Make use of the equalityξ +ξ =ξ (1+ξ ) and Problem 2.23. 3.10.Letrandomvariableξ havethestandardlog-normaldistribution.Forwhich values of parameterα > 0, doesP{ξ +ξ > x}∼P{ξ > x}as x→∞? α 3.11.How do Pitman’s criteria work (i) for the Pareto distribution; (ii) for the exponential distribution? 3.12.Specify Kesten’s bound for the standard Cauchy distribution. 3.13.LetX(t)beacompoundPoissonprocesswithasubexponentialdistribution ofjump.Foreveryt,ï¬ndtheasymptotictailbehaviourofthedistributionofX(t) in terms of the jump distribution. 3.14. Find an example of subexponential distribution F and of counting random variableτ such that the equivalence ∗τF (x)∼EτF(x) as x→∞ doesn’t hold. Hint: Make a link to Galton-Watson process.

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### MAT 150 College Algebra

Questions: The Woodmill Company makes windows and door trim products. The first step in the process is to rip dimension (2 × 8,2 × 10, etc.) lumber into narrower pieces. Currently, the company uses a manual process in which an experienced operator quickly looks at a board and determin ...

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### Machine Learning System

 Submission: o 1document in Word/ PPT /PDF o Plus 1document Excel Sheet with details.  IMPORTANT GUIDELINES: o The objective of the project is for you to know in depth of use cases and application of Analytics, Artificial Intelligence & Machine Learning in the company of choice & how it ...

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