In the low alcohol group, 174 women developed head and neck cancer in 23,800 person-years of observation, while in the high alcohol group 126 women developed head and neck cancer in 4,200 person-years.

Breast cancer was diagnosed in 710 women with low alcohol intake who contributed 22,100 person-years of observation, while in the high alcohol intake group 290 women developed breast cancer in 3,900 person-years of observation.

Calculate the attributable risk due to high alcohol intake for head and neck cancers and breast cancers in this cohort of women.

2. There is a large area of Bangladesh where the groundwater is contaminated by arsenic. Residents of this area suffer from elevated rates of cancer, and of pre-cancerous skin lesions, because they often have no alternative but to drink the arsenic-contaminated water. Many efforts are underway to solve this problem. In one study, investigators looked for evidence that the effect of arsenic on pre-cancerous skin lesions might be increased or decreased by other factors – effect modifiers. One such possible factor is pesticide use which is common in this agricultural region. The table shows the results of a 6-year closed prospective cohort study in which residents were followed and periodically examined for the occurrence of pre-cancerous skin lesions. All these people are exposed to arsenic in drinking water, and so this table does not show that exposure. These data divide the cohort into 3 groups based on how long they were exposed to pesticides. a. b. c. d. a. What measure of disease frequency can be calculated in these data? b. Calculate this measure for each of the 3 exposure groups. c. For the group with no pesticide exposure, calculate a 95% confidence interval for the measure of disease frequency. What does this interval mean? d. Calculate a ratio measure of association, comparing the risk of skin lesions in those with less than 7 years of exposure to those with no exposure, and another measure of association comparing those with 7 and over years of exposure to those with no exposure. Interpret these 2 measures of association. e. Is there evidence that pesticide exposure affects the risk of skin lesions in this population? Explain.

Let X ∈ L(U, V ) and Y ∈ L(V, W). You may assume that V is finite-dimensional.

1)Prove that dim(range Y) ≤ min(dim V, dim W). Explain the corresponding result for matrices in terms of rank

2) If dim(range Y) = dim V, what can you conclude of Y? Give some explanation

3) If dim(range Y) = dim W, what can you conclude of Y? Give some explanation

Consider this code: "int v = 20; --v; System.out.println(v++);". What value is printed, what value is v left with?

20 is printed, v ends up with 19
19 is printed, v ends up with 20
20 is printed, v ends up with 20
19 is printed, v ends up with 19
cannot determine what is printed, v ends up with 20

List the eight influence tactics described in this chapter in terms of how they are used by students to influence their university instructors. Which influence tactic is applied most often? Which is applied least often, in your opinion? To what extent is each influence tactic considered legitimate behavior or organizational politics?

The eight influence tactics are silent authority, assertiveness, information control coalition formation, upward appeal, persuasion, ingratiation and impression management, and exchange.

1. Let V and W be vector spaces over R.

a) Show that if T: V → W and S : V → W are both linear transformations, then the map S + T : V → W given by (S + T)(v) = S(v) + T(v) is also a linear transformation.

b) Show that if R: V → W is a linear transformation and λ ∈ R, then the map λR: V → W is given by (λR)(v) = λ(R(v)) is also a linear transformation.

c) Let E(V) be the set of all linear operators T: V → V. Check that E(V) is a vector space with the addition and scalar multiplication defined above.

d) Suppose dim V = n. What is dim(E(V))? Justify your answer.

1. Write the set { x | x ∈ R, x2 = 4 or x
2 = 9} in list form.
2. {x: x is a real number between 1 and 2} is an
a) finite set
b) empty set
c) infinite set
3. Write set {1, 5, 15, 25,…} in set-builder form.
4. What is the cardinality of each of these sets?
a) {{a}}
b) {a, {a}}
c) {a, {a}, {a, {a}}}
d) {∅}
e) {∅, {∅}, {∅, {∅}}}
5. Suppose that A is the set of sophomores at your school and B is the set of students in
discrete mathematics at your school. Express the following set in terms of A and B:
"the set of students at your school who either are not sophomores or are not taking discrete
mathematics"
a. A
c ∩ Bc
b. A
c U B
c
c. B-A
d. A-B
6. Let A be the set of students who live within one mile of school and let B be the set of
students who walk to classes. Describe the set B-A.
a. The set of students who walk to classes but live more than 1 mile away from school.
b. The set of students who walk to classes but live within 1 mile away from school.
c. The set of students who walk to classes.
7. What is the power set of the set {1, a, b}?
8. Let S = {∅, ?,{?}}Determine whether each of these is an element of S, a subset of S, neither,
or both.
a) {?}
b) {{?}}
c) ∅
d) { {∅ }, ?}}
8. Determine whether each of these statements is true or false.
a) 0 ∈ ∅
b) ∅ ∈ {0}
c) {0} ⊂ ∅
d) ∅ ⊂ {0}
e) {0} ∈ {0}
f) {0} ⊂ {0}
g) {∅} ⊆ {∅}
9. Let A = {a, b, c}, B = {x, y}, and C = {0, 1}.
Find A × B × C.
10. Find A2
if A = {0, a, 3}.

An enzyme was found that catalyzes the reaction between students, S and academic success, P (for pass); the enzyme was called studyase.

An enzyme assay was run on studyase. 10μg of studyase (molecular weight 20,000D) was placed in a set of test tubes each of which contained 1mL of the substrate student at varying concentrations and the amount of product, academic success (P) was determined.

The following results were determined:

Note 1mM = 1millimole/L = 1μmol/mL

Plot a Lineweaver-Burk plot of 1/V versus 1/S

Determine Vmax and Km for the enzyme studyase.

Calculate Kcat and the catalytic constant (kcat/km) for the enzyme. (find [E]_T as total μmoles/mL)

Another enzyme called partyase was analyzed and when 0.010 μmoles of this enzyme was assayed it was found to have a Vmax of about 50 μmol/mL/sec and a Km of 5 mM. Calculate Kcat and the catalytic constant for this enzyme.

i.Compare the 2 enzymes on the basis of affinity for the binding site and kinetic efficiency.

Name the distribution which seems most appropriate to each of the following random variables and specify the values of the associated parameters. [Example: “The number of students in a class of size 42 who pass Mech. Eng. 1234, given that, on average, the proportion of students who pass Mech. Eng. 1234 is 0.6”. Answer: Binomial; n = 42, p = 0.6.]

1. (i) The number of digits generated randomly and independently from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} to obtain the first occurrence of “3”.

2. (ii) The number of computers, in a lab containing 20 computers, which fail before their warranty expires, given that 5% of such computers fail before their warranty expires.

3. (iii) The number of Dell computers in a lab containing 20 computers which were chosen at random from a supply of 100 computers, 5 of which were Dells.

4. (iv) The number of reflected sub-atomic particles in an evacuated duct of a nuclear fusion reactor, when 50 particles are released in the duct. For this particular duct, 16% of all such particles are reflected, and 84% of all such particles are absorbed. The particles behave independently of each other.

5. (v) The number of graduate students on a committee of size 5 which is chosen at random from a university department consisting of 15 faculty members and 23 graduate students.

6. (vi) The number of households sampled by a sociologist, who samples until he obtains a house- hold whose head is a single female parent, given that 12% of all households are headed by a single female parent.

7. (vii) The number of deer caught and inspected by Wildlife Officers, up to the time when they catch a tagged deer, given that 1.5% of all deer are tagged.