Probability-Theory-and-Statistics

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  1. Further generalize the Bayesian analysis of medical screening from last week. Let a rare disease D occur with probability P(D) = δ, with δ small. Now suppose that the test has different (but still small) error rates for positive and negative results: P(+|D) = (1 − ε+ ) and P(−|Dc) = (1 − ε−). Derive the probabilities P(Dc|+) and P(D|−). Interpret your results.
  2. In a particular game, you keep rolling a pair of (six-sided) dice until the sum comes up either “7” or “11”; once this happens you stop (and someone else rolls). Let Ri be the event that you stop after roll number i. Calculate P(R1) and P(R2), and find a general formula for P(Rn).
  3. In a five-card poker hand, what is the probability of getting “two pair,” with two cards of the same kind, two cards of a different kind, and one card of a third kind?
  4. Derive the multinomial coefficient for the number of ways to divide n objects into three groups of n1, n2 and n3 objects, with n1 +n2 +n3 = n; second group.) Confirm that this reduces to the usual binomial coefficient when n3 = 0.
  5. (Mendelian genetics.) Pea plants have green seeds or yellow seeds. The color is controlled by two genes, one from each parent plant, with yellow (y) being dominant over green (g). A gg plant has green seeds, yy has yellow, and the hybrids yg and gy have yellow seeds. In the wild, the four types {yy,yg,gy,gg} are equally likely.
    1. (a) Two wild plants with yellow seeds are randomly selected and bred to give a first generation of plants. What is the probability that a first-generation plant has yellow seeds? What is the probability that it has yy genes?
    2. (b) Two first-generation plants with yellow seeds are randomly selected and bred to give second-generation plants. What is the probability that a second-generation plant has yellow seeds? What is the probability that it has yy genes?
  6. A Starburst candy package has 12 pieces, three each of four flavors: berry, lemon, orange and cherry. The pieces are arranged randomly in the pack. You draw the first four from the pack. (a) What is the probability that all four are different flavors?
    (b) What is the probability that your four pieces have exactly two each of two flavors? (c) What is the probability that your four pieces include all the flavors but lemon?

n n! n,n,n =n!n!n!

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(Hint: first divide the n objects into groups of n1 and n − n1 objects, and then subdivide the

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Comment 19912403

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As we learned this week, Knowledge Translation (KT) has been practiced and implemented by Indigenous communities throughout their history. Now that KT is being recognized as a fundamental step in research and policy development in the Western world, we can begin to bridge a gap, or develop meaningful relationships, between researchers, policymakers and Indigenous communities. The one fundamental consideration in KT that needs to be recognized is that Indigenous communities have important knowledge to share when it comes to research and policy development. Their contributions need to be respected and taken seriously.

When preparing to conduct KT in an Indigenous context it is important for a researcher to follow the fundamental phases of community-based participatory research. There needs to be active and continuous involvement from the Indigenous community that is being researched. Without this, there is a potential that the results of the study are not relevant or cannot be applied to policy development in that community. There could be skewed data due to researchers not measuring the correct targets or asking the wrong questions. This can completely stop the process of KT from even occurring as the knowledge gained from the study will not be able to provide that community with a relevant policy or program. This partnership needs to take place in order for meaningful research and policy development to occur. Indigenous communities need to have an active participatory role in research and policy development from the very beginning to the very end. This includes upholding the principles of the 4 R’s of research, OCAP and KT.

Researchers and policymakers need to understand that KT is not meant to be a one and done approach. Collaboration and communication will be an ongoing process. Once research, or KT on a policy front takes place, there needs to be a sustained relationship. Communities evolve, they are not stagnant. Policy or programming will need to be adapted overtime. This is why a sustained relationship needs to take place to ensure the effectiveness of policy or programming is maximized.

If knowledge, or research, is being translated from other communities or contexts, the researchers or policymakers need to understand that Indigenous communities are not homogeneous. There is not a one size fits all approach when applying knowledge to policy or practice for Indigenous communities. Each community has their own needs. Each community will need meaningful consultation to ensure the way the knowledge is implemented is actually respectful and relevant to their community.

When presenting knowledge to communities it is especially important to tailor the message correctly. When a new policy or program is being implemented for an Indigenous community, it is important that community leaders can take hold and foster the messaging. Indigenous community leaders know their community best, will know how to promote messaging, and educate their community.

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Project section and Evaluation for the final paper

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Submit your thesis including the 5-6 pages of the Project section and Evaluation you have been developing for the past several weeks. See the guidelines listed below for the Project section.

CLICK on the link to submit your Assignment. See the Rubric attached to the assignment for guidance. DO NOT USE BOOKS-Instructors cannot verify those sources (if you must use a book-keep to a minimum-AND scan/copy/paste the actual content and provide it to the instructor. Recommend you use articles from WU Library databases.

Following the Methodology chapter will be the Project chapter. This chapter will consist of at least five pages of dialogue on how you designed your project and how you plan to implement it.


I have attached the my paper that you has the topic that you need to develop. and for your reference I have attached another peer’s paper that you can use as reference for to add those sections.

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please write this essay 1

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I will post all requirement here, just follow it and we use turnitin, so 100% original
6 pages pls
 
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