STATISTICS

1. Consider the continuous time Markov chain model for a single server queue with a modification that allows for arrivals in pairs. The arrival rate is A and the service rate is p, but each arrival, with probability 0, is of a pair of individuals rather than a single individual. The corresponding continuous time Markov chain model for the queue size has as its state space the set of all non-negative integers and the following transition rates:
transition rate A(1-0) (i>0) i-*i+2 AO (i>0) i ó 1 IL (i >1)
where A > 0, p > 0 and 0 < < 1.
(i)
Write down an expression for the mean number of individuals who arrive per unit time. [1] (ii) Write down a formula for the traffic intensity of the queue and explain on intuitive grounds why the condition
A(1 + <
should be necessary and sufficient for the existence of an equilibrium distribu-tion. [2] (iii) Write down the balance equations for the equilibrium distribution (iri : i > 0). Show why the detailed balance equations cannot be valid for this model, except in the special case 0 = 0. [5] (iv) Prove from the balance equations that the equilibrium distribution, if it exists, satisfies the difference equation
Intl = + ACM-2 > 2).
What additional conditions would you use to determine the equilibrium distri-bution? [7] (v) Assuming the existence of an equilibrium distribution, sum the equations of Part (iv) over i to find an expression for wo. Deduce that the condition of Part (ii) emerges again as the condition for the existence of an equilibrium distribution. [5]

Psychology health promotion

You are required to develop an intervention proposal to satisfy learning outcome 2:
Prepare a report describing the development, implementation and evaluation of a health promotion intervention (2000 words)

Your report should be prepared for a hypothetical client e.g. Head teacher at a local primary school, who is interested in but has not yet commissioned the intervention.
Your report should consider the following issues:
ïNeeds Analysis
ïThe health risk
ïWhy is an intervention necessary
ïDevelopment of the intervention
ïType of intervention ñ what works in which environment
ïTheoretical underpinning/mechanisms
ïMaterials (you do not have to develop the materials)
ïIntervention implementation plan
ïTimeframe of intervention
ïConsideration of resources (you do not have to address costs)
ïEquipment
ïStaffing
ïEvaluation
ïProcess evaluation
ïOutcome evaluation
Your report should be evidence-based (to demonstrate breadth of reading and familiarity with relevant literature) and referenced throughout.

Word limit: 2000 words (excluding references)
Coursework intervention report model answer

The general requirement for a good answer is to:
ï Be well-written, showing evidence of critical insight and sound argument
ï Show reading of relevant material and an ability to integrate this material into the answer in a well-structured and effective manner.

A passing answer must attempt to:
ï Describe a specific health risk relevant to particular population/context supported by current research
ï Describe a psychologically derived health promotion intervention aimed at addressing the identified health risk
ï Draw on appropriate psychological theory and research to justify the approach adopted
ï Consider the relevant resources required to implement the intervention
ï Identify at least one method of evaluation to assess the success of the intervention

Furthermore, a good answer will include one or more of the following:
ï Present a sophisticated discussion of a specific health risk relevant to particular population/context supported by current research
ï Describe a theoretically derived and psychologically orientated health promotion intervention aimed at addressing the identified health risk
ï Provide a clear diagram outlining the implementation of the intervention
ï Draw on appropriate health promotion and health psychology theory and research to justify the approach adopted
ï Consider the range of resources required to implement the intervention (human and physical)
ï Identify multiple methods of evaluation to assess the success of the intervention at different stages

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