1.Exercise 4) A fair coin is tossed. If it lands heads, a fair four-sided die
is thrown (with values 2,3,4,7). If
2,3,4,7). If it lands tails, a fair six-sided die is
thrown (with values 3,4,5,6,7,9). Regardless of which die is used, Alice
eats n grains of rice, where n is the largest prime factor of the die result
(for example, the largest prime factor of 9 is 3).
(a) What is the conditional probability that the coin lands heads, given
that Alice eats three grains of rice?
(b) Suppose that the entire experiment is conducted twice on the following day (starting with a new coin toss on the second run-through).
What is the conditional probability that the coin lands heads on both
run-throughs, given that Alice eats a total of five grains of rice during the two run-throughs?
(Do not count the two grains from part (a) in part (b); we assume
two brand new experiments, each with a new coin toss. Start your
solution by defining a suitable partition of the sample space. Please
use an appropriate notation and/or justification in words, for each
value that you give as part of your solution.)
Exercise 5) Alice and Bob throw an unfair coin repeatedly, with probability 2/5 of landing heads. Alice starts with £2 and Bob starts with £3 .
Each time the unfair coin lands heads, Alice gives Bob £1 . Each time
the unfair coin lands tails, Bob gives Alice £1 . The game ends when one
player has £5 .
(a) Draw a labelled Markov chain describing the problem, and write
down a transition matrix P. Write down the communication classes,
and classify them as either recurrent or transient.
(b) Using the transition matrix, calculate the probability that Alice loses
all of her money in exactly four tosses of the unfair coin.
(c) Calculate the (total) probability that Alice loses all of her money
(before Bob loses all of his).
(d) Calculate the expected (mean) number of tosses of the unfair coin,
for the game to end.
2.students are expected to research and compose a paper based on the application of concepts and theories examined in class.
ies examined in class. This paper is not a literature review, though a literature review is part of your work. As this course takes place in a compressed timeline, I provided some suggestions for research topics. Feel free to use one of these as a springboard or propose your own.
At the end of the second week of class, students submit a three-page research paper prospectus. A research prospectus is a preliminary plan for conducting a study. This is not a detailed and technical research proposal, but rather, an analysis of the issues likely confronted in such a study. In essence, it is a preliminary proposal of work.
Research Paper Prospectus Elements
To complete the Research Paper Prospectus, consider the following elements. While the prospectus is limited to three pages of body content, remember, students must cover each of these areas as relevant to the plan for research:
Research Problem. What is the research problem? A problem is a situation when left untreated, produces a negative consequence for a group, an institution, or a(n) individual(s). What makes it a problem? For whom? Who says so?
Assumptions. On what assumptions is the work based? Which assumptions are verifiable in literature? Which assumptions are speculative?
Theoretical Issues. What theoretical issues arise from the study? For example, "theoretically," how is the problem and suspected results explained to other scholars? Is there a behavior view? A social systems view? Are there other theoretical orientations to consider in the study's design?
Literature Review. What, in general, does the literature say about the topic? While more development is expected for the final paper, a review of major theories, research, and writers in the field is needed.
Research Questions. Based on the problem, what are the research questions to be answered? How and why will answering the questions contribute to solving the research problem? Remember....a research question can only be answered with empirical data or information.
General Research Plan. In general, what research is necessary to answer the research question. What kind of data is needed? Specify the type, such as surveys, observations, or interviews. Who is to be studied and why? How is the data reduced and made sense of? How is the quality of the data assured?
Anticipated Difficulties and Pitfalls. What kind of difficulties and pitfalls are expected in a study of this nature? What can be done to prevent them or minimize their effects?
Anticipated Benefits. Who will benefit from the fact this research is undertaken? How? Why? Who might be disturbed by this proposed study? How? Why?
Paper Format Requirements
The Research Paper Prospectus is presented in standard APA 7 format, with a cover page, running head, body, and references list. The cover page and references do not count toward the three-page requirement. The body uses headers and in-text citations in the manner prescribed by APA. Students should include any references they know at the time they submit the prospectus, though it is expected the references may change or increase in number. Full and complete adherence to APA is required.
As APA format is the rule, remember the formatting rules shown on the Sample Paper (Links to an external site.):
Times New Roman, 12pt
1" margins on all sides
Double spaced, with extra line spaces removed (see below)
Page numbers in the upper right
Two spaces after concluding punctuation
150-250 word abstract with keywords
APA-style in-text citations and quote format. Use the Purdue OWL in-text citation information (Links to an external site.)to help you.
Alphabetical (by author) reference page with correct reference format. DO NOT trust the reference generator in your word processing program. It is WRONG! Use the Purdue OWL references information (Links to an external site.)to correctly structure references and do so manually.
3.Directions: You are part of a fireworks crew assembling a local fireworks display.
There are two parts to the fireworks platforms:
rts to the fireworks platforms: one part is on the ground and the
other part is on top of a building. You are going to graph all of your results on one
coordinate plane. Make sure to label each graph with its equation. Use the following
equations to assist with this assignment.
• The function for objects dropped from a height where t is the time in
seconds, h is the height in feet at time it t, and 0 h is the initial height is
0 ht t h ( ) 16 =− + .
• The function for objects that are launched where t is the time in seconds, h is
the height in feet at time t, 0 h is the initial height, and 0 v is the initial velocity
in feet per second is 2
0 0 ht t vt h ( ) 16 =− + + .
Select the link below to access centimeter grid paper for your portfolio.
Centimeter Grid Paper
First, conduct some research to help you with later portions of this portfolio
• Find a local building and estimate its height. How tall do you think the
• Use the Internet to find some initial velocities for different types of fireworks.
What are some of the initial velocities that you found?
Respond to the following items.
1. While setting up a fireworks display, you have a tool at the top of the
building and need to drop it to a coworker below.
a. How long will it take the tool to fall to the ground? (Hint: use the first
equation that you were given above, 2
0 ht t h ( ) 16 =− + . For the building’s
height, use the height of the building that you estimated in Task 1.)
b. Draw a graph that represents the path of this tool falling to the
ground. Be sure to label your axes with a title and a scale. Your graph
should show the height of the tool, h, after t seconds have passed.
Label this line “Tool”.
The Indigo Insurance Company is a large company based in Melbourne. Several years ago, an email survey of all their
survey of all their employees found that employees were required to respond to an average of 50 work-related emails per week with a standard deviation of 1.5 emails per week. However, an employee advocacy group believes the average number of work-related emails Indigo Insurance Company employees are now required to respond to is more than 50 emails per week.
To investigate this further, the employee advocacy group took a random sample of 20 staff employed by Indigo Insurance Company during the second week of March 2018,and asked these employees to record the number of work-related emails to which they were required to respond.
(b). What does the highlighted section of the distribution in Figure 1 represent?
(c). The random sample of 20 employees of Indigo Insurance Company taken by the employee advocacy group turned out to have a mean of 50.8 work-related emails to respond to in that week. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your answer.
(d). Given the sample was randomly selected and that the number of work-related emails each employee was required to respond to was recorded accurately, what conclusion can we reach from part (c)?
To answer questions (b) to (d), consider the sampling distribution shown in Figure 1.
6.A uniform beam of length L
and mass m shown in Figure
P12.16 is inclined at an angle
u to the horizontal. Its
izontal. Its upper
end is connected to a wall by
a rope, and its lower end rests
on a rough, horizontal sur-
face. The coefficient of static
friction between the beam
and surface is ms. Assume
the angle u is such that the static friction force is at its
maximum value. (a) Draw a force diagram for the beam.
(b) Using the condition of rotational equilibrium,
find an expression for the tension T in the rope in
terms of m, g, and u. (c) Using the condition of trans-
lational equilibrium, find a second expression for T in
terms of ms, m, and g. (d) Using the results from parts
(a) through (c), obtain an expression for ms
vertical component of this force. Now solve the same
problem from the force diagram from part (a) by com-
puting torques around the junction between the cable
and the beam at the right-hand end of the beam. Find
(e) the vertical component of the force exerted by the
pole on the beam, (f) the tension in the cable, and
(g) the horizontal component of the force exerted
by the pole on the beam. (h) Compare the solution
to parts (b) through (d) with the solution to parts
(e) through (g). Is either solution more accurate?
19. Sir Lost-a-Lot dons his armor and sets out from the
castle on his trusty steed (Fig. P12.19). Usually, the
drawbridge is lowered to a horizontal position so that
the end of the bridge rests on the stone ledge. Unfor-
squire didn’t lower the draw-
ing only the angle u. (e) What happens if the ladder
is lifted upward and its base is placed back on the
ground slightly to the left of its position in Figure
8.I have the following budget constraints for an agent. In the first period of his life, he only can get
et loans (he doesn't "earn" income). With the loans (L) he needs to decide between first period consumption (C1) and investment (I). The amount invested will allow him to get a second period income Y with probability P which is increasing in I (therefore, P(I)), In case of success and the person obtain Y, the individual should use Y to repay the loan (L) that he requested in the first period and consume in the second period (C2). However, with probability 1 - P(I), the person don't get Y and therefore only consume C1. Note that if the individual only invest the loan (L=I) and don't obtain Y, he can't consume anything. That motivates him not to invest the whole loan and keep part of the loan in order to warrant at least first period consumption. Therefore, considering B the parameter for the time preference, the problem would be:
max U=ln(C1) + Bln(C2)
s.t: L = I + C1
Y(I) = L(1+r) + C2
with Probability P(I)
s.t: L = I + C1
with probability 1 - P(I)
My question is, Have you ever seen something like this? If yes, how to proceed? What is more important, I really need a bibliography (a book or article talking about this)