You collect several thousand Drosophila melanogaster individuals from the UC Davis experimental orchard in Winters. Youuse1000 of these flies to establish a laboratory population, which you maintain at a census population size of 1000 each generation. You then establish from the remaining field-collected flies a series of replicated populations of size 10, 100, 200, and 500and maintain each at the starting size (10, 100, 200, 500) for several generations. After some time, you sequence each lab population.

a. If one plotted for each lab population, the frequency of each nucleotide variant vs. its true frequency in the UCD population, how would the correlations differ across lab populations?

b. Which lab populations do you think would provide the best estimate of the true UCD frequencies? Why?

c. Now imagine that one carried out the same type of correlation analysis of allele frequencies ,but instead of comparing each population to the true UCD frequencies you compare the allele frequency of the replicated populations to each other (e.g., the populations of size 10 are compared to one another, the populations of size 100 are compared to one another, etc.). How would the pairwise correlations of frequency vary from one population size to another?

d. What two aspects of the sampling of flies in this entire experiment would lead to allele frequency deviations from the true UCD frequencies for sites free of natural selection?

e. You measure sequence divergence between each lab population and the sibling species, Drosophila simulans. How will the expected divergence vary across replicated populations of different size? Why?

A group of 400 students that lived in on-campus housing were surveyed and asked if (1) they had access to a car and (2) whether they owned a television. Suppose that a person collecting the data likes puzzles and she has given you the following information about the results of the poll. One hundred thirty of the students responded that they had access to a car, 240 students did not own a television, and 150 students both did not have access to a car and did not own a television.

A. Define the minimum number of basic sets needed to create the Venn diagram. (3 points)

B. Write out the set theoretic notation for each piece of information that gives information about the number of students who responded to the various characteristics listed in the problem. (4 Points)

C. Create the appropriate Venn diagram created using the above information. Define the minimum number of appropriate sets needed to answer this problem. (3 points)

D. Write out a short step-by-step explanation (Step 1, step 2, step 3, …) on how you found the values for each of the basic regions in the Venn diagram in the order that you found them. Include any calculations that you may have made in various steps. Use proper mathematical notation for the sets and the number of elements in the set of interest. Refer to the basic regions using the Roman numerals that are in Figure 1 (b) on page 201. (5 points)

E. List the answers to the following questions:

i. How many student owned a television but did not have access to a car? (1 point)

ii. How many students only had access to a car? (1 point)

The output voltage of a power supply unit has an unknown distribution. Using a sample size of 36, sixteen samples are taken with the following sample-mean values: 10.35 V, 9.30 V, 10.00 V, 9.96 V, 11.65 V, 12.00 V, 11.25 V, 9.58 V, 11.54 V, 9.95 V, 10.28 V, 8.37 V, 10.44 V, 9.25 V 9.38 V and 10.85 V. Let µ and σ² denote the mean and the variance of the output voltage of the power supply unit. (a) What distribution describes the sample-mean? What are the parameters of the distribution (in terms of µ and σ² )? (b) Test the hypothesis that the population variance σ² = 36 V² at 95% confidence. (c) Construct a two-sided 95% confidence interval for the population’s standard deviation.

7-5) A researcher intends to determine if exposure to a documentary about death penalty would impact attitudes toward capital punishment. From a large class of undergraduate students she selects a random sample of 40 students who will watch the movie [experimental group] and a random sample of 40 students [control group] who will not watch the documentary. She then measures one’s opposition toward penalty using a single-item question asking students to rank their opinions on a scale from zero [strong support for death penalty] to six [strong opposition]. The table below presents the summary results of her experiment:

                                             N            Mean     Std. dev.

Experimental group         40           4.0         2

Control group                   40           3.0         1.5      

a.            Formulate the null hypothesis

b.            Formulate the alternative hypothesis

c.            Using the independent-sample t test, test the null hypothesis [H0]

d.            List the value of the critical t you used to test H0 [df = n1 + n2 – 2; p = .05; 2-tail test]

e.            Reach a statistical conclusion using p = .05, 2-tail test, and the appropriate df

f.            Interpret your results. In your opinion did the documentary had an effect or not? Explain.     

1) Create a table “college” that has as attributes name, city name, state/province/region name, country name, and year in which the college was established as well as an ID as primary key. Insert records for 5 colleges of your choice, including one or more you have attended.

2) Create a table “student” that has as attributes first name, last names, and college ID for students, and insert the names of yourself and friends who attended one or more colleges together with you (if you have only attended one college, the name can be the same for all). Note that the student names can be fictitious but not the college name.

3) Add a foreign key to the appropriate table above, using “on delete cascade” as referentially triggered action, and demonstrate that insertion for a student record with a non-existing college ID fails.

4) Do a query that shows all students together with their respective college information. For colleges, that no students have attended, list all student information as null (i.e. OUTER JOIN).

5) Do a query that lists college names together with the number of students in the database that have attended that college, using the GROUP BY statement.

6) Do a query of catalog information.

7) Do a deletion of a college that was referenced and redo the query from question 4.

QUESTION 1

Vector Space Axioms

Let V be a set on which two operations, called vector addition and vector scalar multiplication, have been defined. If u and v are in V , the sum of u and v is denoted by u + v , and if k is a scalar, the scalar multiple of u is denoted by ku . If the following axioms satisfied for all u , v and w in V and for all scalars k and l , then V is called a vector space and its elements are called vectors.

1) u + v is in V

2) u + v = v + u

3) (u + v) + w = u + (v + w)

4) 0 + v = v

5) v + (−v) = 0

6) ku is in V

7) k(u + v) = ku + kv

8) (k + l)u = ku + lu

9) k(lu) = (kl)(u)

10) 1v = v

Task: Show that the set V of all 3×3 matrices with distinct entries and also combination of positive and negative numbers is a vector space if vector addition is defined to be matrix addition and vector scalar multiplication is defined to be matrix scalar multiplication.

QUESTION 2

Suppose u, v, and w are all vectors in a vector space V and c is any scalar. An inner product on the vector space V is a function that associates with each pair of vectors in V, say u and v, a real number denoted by u, v that satisfies the following axioms.

(a) < u, v > = < v, u > (Symmetry axiom)

(b) < u + v, w > = < u, w + v, w > (Additive axiom)

(c) < cu, v > = < c u, v > (Homogeneity axiom)

(d) < u, u > ≥ 0 and < u, u > = 0 if and only if u = 0 (Positivity axiom)

A vector space along with an inner product is called an inner product space.

Task: Show that the set V of all 3×3 matrices with distinct entries and also combination of positive and negative numbers is a inner product space if vector addition is defined to be standard matrix addition and vector scalar multiplication is defined to be matrix scalar multiplication.

Let (V, ||·||) be a normed space, and W a d^Norm_V,||·|| -closed vector subspace of V.

(a) Prove that a function |||·||| : V /W → R_≥0 can be consistently defined by ∀v ∈ V : |||v + W||| df= inf({||v + w|| : R_≥0 | w ∈ W}).

(b) Prove that |||·||| is a norm on V /W.

(c) Prove that if (V, ||·||) is a Banach space, then so is (V /W, |||·|||)

Think about how your school (or workplace) can become a more culturally sensitive place for students (or employees) from different backgrounds. How can you help everyone feel more welcomed? Develop a list of at least five suggestions to improve cultural acceptance. Explain how you would implement each suggestion at your school (or workplace). You are encouraged to conduct research and reference the textbook to help you generate ideas, however, your ideas must be original. At the end of your list of suggestions, write two paragraphs explaining what you learned from completing this assignment and how you can incorporate some of these suggestions in your major field of study of Online Teaching and Learning.

In 1994 two researchers from the RAND Corporation in Santa Monica, California, studied the market for cocaine. They estimated the average price elasticity of demand for the demand for cocaine to be 0.5 in absolute value. At the time, the federal government was increasing its spending on law enforcement to keep cocaine from getting into the country. The goals were to decrease the use of cocaine due to the public health hazards and to lower the rate of drug-related crime.

Is it likely that the government's increasing its spending on law enforcement accomplished its goals? Explain your answer

Find the concept of Manicheaism that influenced the way the Puritains in Plymouth and the Massachusetts Bay colonies saw the world and their role in it. consider the myths that Europeans held about the New World, such as the Empty Land, myth, how those ideas clashed with the indigenous people who already inhabited the continent. What are the key differences between the early colonies found in St. augustine, Santa Fe, Quebec, and Jamestown and those in New England? What are some of the most notable characteristics of the experiments in a new society that grew out of the migration of the Puritans?