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It is a well-known fact(oid) that armadillos always have identical quadruplets (four offspring). Each of the 4 little armadillos has a 1/3 chance of becoming a doctor, a lawyer or a scientist, independently of its 3 siblings. A doctor armadillo will reproduce further with probability 2/3, a lawyer with probability 1/2 and a scientist with probability 1/4, again, independently of everything else. If it reproduces at all, an armadillo reproduces only once in its life, and then leaves the armadillo scene. (For the purposes of this problem assume that armadillos reproduce asexually.) Let us call the armadillos who have offspring fertile.
What is the distribution of the number of fertile offspring? Write down its generating function.
What is the generating function for the number of great-grandchildren an armadillo willhave? What is its expectation? (Note: do not expand powers of sums)
Let the armadillo population be modeled by a branching process, and let's suppose that itstarts from exactly one individual at time 0. Is it certain that the population will go extinct sooner or later?
You want to create a mileage grid showing the distance between every pair of the 50 U.S. state capitals. How many numbers will you have to compute?
Find the area of the lateral surface over the curve C in the xy-plane and under the surface z = f(x,y), where the lateral surface area is is given by the integral below.
Suppose your friend refused a job offer from the first company on ethical grounds even though he had no other offer. Explain his choice in terms of Kohlberg's six-stage theory of moral development and either defend or criticize it based on your ow..
When we speak, we convey not only information but emotional tone as well. Ambady et al. (2002) investigated the relationship between the emotional tone used by surgeons as they talked to patients and the surgeon's history of being sued for malprac..
Given a sheet of paper 8.5" by 11", fold the top left corner down to a point on the bottom edge. Where should you place this corner to maximize the area of the triangle formed in the bottom Left corner
the distanc3e between points A and B is 50 ft. Angle A measures 70 degrees, and angle B measures 65 degrees. A bridge will be built between points A and C.
Which of the following would be a valid tensor equation? You should indicate if the equation is valid; and if it is not valid, you should state why.
Suppose you have a square yard that is x feet on each side. Suppose you put a 2 1/2 foot sidewalk around the edge of this yard, reducing the area of the yard. What is the new area of the yard? What is the total area of the sidewalk?
An economy has three sectors: A, B, C. Sector A sells 20% of its output to B and 30% to C and retains the rest. Sector B sells 30% of its output to A and 40% to C and retains the rest. Sector C sells 50% of its output to A and 30% to B and retains..
Which of the following could be a linear programming objective function?
Plot x.vs. x for h = a12/4a2, h a12/4a2 , What is the significance of h = a12/4a2 with respect to the phase diagrams?
Which of these measures of central tendency do you think most accurately describes the lifestyle variable you are looking at?
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