Let ? be the sample space of an experiment and let ℱ be a collection of subsets of ?.

a) What properties must ℱ have if we are to construct a probability measure on (?,ℱ)?

b) Assume ℱ has the properties in part (a). Let ? be a function that maps the elements of ℱ onto ℝ such that

i) ?(?) ≥ 0 , ∀ ? ∈ ℱ ii) ?(?) = 1 and iii) If ?1 , ?2 … are disjoint subsets in ℱ then ?(⋃ ??) = ∞ ?=1 ∑ ?(??) ∞ ?=1 . Show that 0 ≤ ?(?) ≤ 1, ∀? ∈ ℱ.

c) Is every subset of ? necessarily an event? Explain briefly. Rigorous definitions are not necessary.

d) Assume ℱ has the properties in part (a). Let ? and ? be any two subsets of ? that are elements of ℱ.

i) Show that (? ∩ ?) ∈ ℱ.

ii) Show that (? ∖ ?) ∈ ℱ, where (? ∖ ?) is the set of outcomes that are in ? but not in ?.

iii) Show that (? △ ?) ∈ ℱ, where (? △ ?) is the set of outcomes that are either in ? or in ? but not in both.

iv) Let ?1 , ?2 , ?3 … be elements of ℱ. Show that ⋂ ?? ∞ ?=1 ∈ ℱ

As an engineer you are responsible to in charge to conduct an experiment for this traffic flow analysis: At 2:00 P.M. a traffic accident closes a road to all traffic. At 2:15 P.M. the road is partially opened with a capacity (car departs) of 1,500 veh/h. Finally, the wreckage is removed, and the road is restored to full capacity (car departs) (3,500 veh/h) at 2:35. From 2:00 to 2:35, car arrives at a constant flow of 2,500 veh/h and then drops to 2,000 veh/h thereafter. Assume D/D/1 queuing to determine

1. Total delay: __________ veh-min

1. Longest vehicle delay under LIFO _________ min

1. Time of queue dissipation: ___________ min

Queue length at 60 min: ___________veh

1. Longest (max) wait of any vehicle (assuming FIFO): ____________min

1. Longest (max) queue length: ____________ veh

1. how a graphical representation of the solution and clearly label the parameters and axis with the appropriate units accordingly.

The results of a tensile experiment on a metal is given in the table below. The tensile sample had circular cross section with the diameter of 10 mm and initial gauge length of 60 mm. Use this table and calculate:

(a) The Young modulus of this metal (in GPa)

(b) The modulus of resilience (MJ/m3 )

(c) The measured diameter of the sample is 9.5mm when the applied force is 37306N. What is the Poisson’s ratio?

(d) What is the engineering stress and strain, as well as the true stress and strain at the applied force of 37306N?

An experiment was performed to determine the efficiency of a transformer. A coil is placed into another coil, and a steel bar is placed on the inside of both coils.

f (efficiency) = V1*N2 / V2*N1

Suppose we ignore the possibility of someone having miscounted the number of turns. Why might "1 turn" (or, perhaps, "1/2 turn") still make sense as an uncertainty on the number of turns?

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 52.0 km due north. A detector is placed 107 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector.

(a) When properly aligned, what angle should the normal to the surface of the mirror make with due south?

(b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.005

The Immortal Life of Henrietta Lacks Book Discussion

In a perfect world, race, ethnicity and culture would have no negative effect on the medical care we receive, but they often do. The effect is due to historical heritage more than skin color. What is meant by this statement? Provide examples (more than one) with page references where historical heritage affects the ability of the family in the book to negotiate the healthcare system. Consider health literacy, communication, ethics, and health disparities. You will also identify one resource that helps others to understand the concept that you are writing about in this discussion. You must explain why this resource is useful and why we should care about what the author(s) have to say. Note: a web page with multiple authors is not an appropriate resource for this assignment.

1. This assignment marks the last part of the course project. In this section, you are to again through the use and application of credible sources author an original discussion post defining, discussing and applying the HR topic posed.
2. Your discussion board submission address the following topic points:
3. Define and discuss the importance of the performance evaluation process using credible sources to support your findings.
4. Using real examples from businesses or HR-related sources found on the internet identify and discuss the; performance evaluation methods and tools that would be appropriate for the employment position chosen in section one of your project.
5. Conclusion:
   1. Explain why your final HR processes and programs are sufficient to use as it relates to the employee life cycle.
   2. Explain the potential issues or concerns that exist when organizations choose not to use job descriptions.

Briefly identify and explain the significance of any 5 of the following items. A
short paragraph (2-4 sentences) should be sufficient in nearly all cases. In the case of a
quotation, please identify the author and explain what theory or principle it illustrates or
exemplifies.

1. GE Moore.
2. The Prisoner’s Dilemma.

3. “Then it must follow that no one willingly chooses to do evil or what he thinks to
be evil.”
4. Ruth Benedict.
5. “Over himself, over his own mind and body, the individual is sovereign.”
6. Karl Menninger.
7. Retributivism.
8. Peter Singer.
9. “We thus conclude that virtue or excellence is a characteristic involving choice,
and it consists in observing a mean relative to us, a mean which is defined by a
rational principle . . . . It is the mean by reference to two vices, the one of excess,
the other of deficiency.”

In the New York Times article, “From Prison to Ph.D.: The Redemption and Rejection of Michelle Jones,” the author describes how an Indiana prisoner who murdered her 4-year-old son 20 years ago became a scholar and was awarded a PhD while still in prison. Following her application to attend further study at Harvard University, she was turned down by Harvard’s administration, citing concerns that they were supporting someone who is a convicted “child murderer.” Elizabeth Hinton, one of the Harvard historians who backed Ms. Jones, called her “one of the strongest candidates in the country last year, period.” The case “throws into relief,” she added, the question of “how much do we really believe in the possibility of human redemption?” Discuss.