7. The following 4-state Markov model with constant intensities a, ß and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, B.y) for these data and hence find the maximum likelihood estimates of a,ß and y.

he National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected. ACC Big Ten PAC-12 SEC CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition Florida State 4 Iowa 9 USC 1 Florida 2 Clemson 5 Michigan St 10 Oregon 6 Alabama 3 Miami 7 Nebraska 14 Oregon 15 Kentucky 8 Georgia Tech 13…

The National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected. ACC Big Ten PAC-12 SEC CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition CollegeAttended ProjectedDraftPosition Florida State 4 Iowa 7 USC 2 Florida 1 Clemson 5 Michigan St 10 Oregon 9 Alabama 3 Miami 6 Nebraska 12 Oregon 15 Kentucky 8 Georgia Tech…

Scenario 3. A researcher creates a new program for college students to reduce feelings of loneliness and enhance students' engagement on campus. This new program helps students to find student groups and clubs that fit their interests. She randomly assigns students to either enroll in this new program (the experimental group) or to not enroll in the program (the control group). She compares students' feelings of engagement between the two groups, and expects that engagement will be higher among the students that are in the program.   What is the most appropriate test statistic to use to test the hypothesis in scenario 3? A) z-test B) z-score C) Independent samples t-Test D) Correlation Coefficient E) One-way ANOVA F) Dependent samples t-Test G) Factor Analysis H) Structural Equation Model   What is the null hypothesis for scenario 3? A) H0: engagement in the experimental group ≤ engagement in the control group B) H0 : engagement in the experimental group = engagement in the control…

In an article in the Journal of Marketing, Bayus studied the differences between "early replacement buyers" and "late replacement buyers" in making consumer durable good replacement purchases. Early replacement buyers are consumers who replace a product during the early part of its lifetime, while late replacement buyers make replacement purchases late in the product's lifetime. In particular, Bayus studied automobile replacement purchases. Consumers who traded in cars with ages of zero to three years and mileages of no more than 35,000 miles were classified as early replacement buyers. Consumers who traded in cars with ages of seven or more years and mileages of more than 73,000 miles were classified as late replacement buyers. Bayus compared the two groups of buyers with respect to demographic variables such as income, education, age, and so forth. He also compared the two groups with respect to the amount of search activity in the replacement purchase process. Variables compared…