(4) (1 point) A random walk is given by:  

2. (6 points) Consider the autoregressive (AR) random process. It is a WSS random process with zero mean and evolves according to the following defining recursive difference equation

6. (8 points) Let

(2) (1 point) Gaussian white noise in continuous time is described by a constant power spectral density for

5. (8 points) Given two jointly WSS processes and with zero mean and a constant frequency

3. (5 points) (a) (2 points) The transition probability matrix of a two-state Markov chain is given by

Earl (age 28) and Velma (age 27) are currently planning for their future family and decide to obtain genetic testing before having children. Earl knows that Cystic Fibrosis runs in his family, and has concerns about having a child with Cystic Fibrosis. Cystic Fibrosis is an autosomal recessive disease, which means that a person can carry the genetic trait, but not have the disease. If both parents carry the trait, then there is a 1 in 4 chance that the child will have the disease. Earl does not have Cystic Fibrosis, but he wonders if he may be a carrier for the genetic trait. Velma was adopted, so she does not know her family’s genetic history. Cystic Fibrosis is a disease that causes damage to the lungs, digestive system and other organs in the body. There is no cure, but there are treatments to manage the disease. People who are diagnosed with Cystic Fibrosis (CF) may take medications, and often have shorter lifespans.   Part A) Explain what information Earl and Velma should know about carrier testing for Cystic Fibrosis (CF). Be sure to address: What key information should they know about carrier testing? Explain the potential benefits; risks; and limitations of carrier testing.   Part B) Imagine Earl and Velma find out with certainty that they are both carriers for CF. Now Earl and Velma must make a decision what to do with this information. First, explain how the information from the carrier testing for CF is actionable. Second, take on either the role of either Velma or Earl to explain what the best course of action is here. Velma thinks that using technologies such as IVF and preimplantation genetic diagnosis to sort through embryos and select an embryo without the CF mutation is the optimal decision. Earl thinks they should conceive children naturally, and believes that they can plan accordingly. Earl believes that using IVF and discarding embryos is reflective of eugenics and unethical. Support your answer with course materials, principles, and concepts from the readings.

Roger and Betty are using IVF to create embryos to have children at Primo Fertility Clinic. Roger and Betty both have Achondroplasia (hereditary dwarfism). They tell Dr. Smith they want to choose two embryos to implant that also have the trait for Achondroplasia, because they want their children to share the same trait and culture that dwarfism provides. Primo Fertility Clinic has a policy that supports a child’s Right to An Open Future. To explain the Right to an Open Future Policy, Dr. Smith would tell Roger and Betty:

Gertrude is on a crusade to expose the risks that IVF entails to women and children, including the higher risk of birth defects and illness in children born using IVF. She is on her third YouTube video called, “Fallacies of The Interest in Existing Argument.” She states, “It is not better to be born with a disability from using IVF than not to be born at all.” Based on the readings, which of the following characterizes Gertrude’s position?

Marvin, an avid rock climber, falls from the top of the mountain and is lying unconscious and immobile. EMTs rush Marvin and his wife Prudence in an ambulance to the hospital. Dr. Jones tells Prudence that it appears Marvin sustained a complete, total, and irreversible neurological injury. Marvin is connected to a ventilator and his heart is beating. Dr. Jones begins clinical tests to determine if Marvin has suffered brain death. Based on the law and clinical standards, which of the following is accurate?