Category: Mathematics

Discuss and compare the probability of the two selected events. Did the results surprise you?

Assignment: Discussion Question:

Probability is all around us. For example, you have probably heard the saying, “You have a better chance of getting struck by lightning than you have at winning the lottery”, but have you looked at the numbers (statistics) or have you taken their word for it?

For the discussion, find the probability of two events that are unlikely to happen: getting struck by lightning, winning the lottery, being attacked by a shark, creating a perfect March madness bracket, etc. Discuss and compare the probability of the two selected events. Did the results surprise you?

Do you think you obtained a random sample (did everyone/thing in the population have an equal opportunity to be surveyed)? Explain.

The aim of the study is to find out if there is an association between body weight and calorie intake.

The aim of the study is to find out if there is an association between body weight and calorie intake.

Is the daily calorie intake associated with an increased risk of obesity (increase in body weight)?

Data must have 30+ samples pieces of data (included in the attachment, survey data with survey questions)

Write a paragraph to answer the following questions: What was the purpose of your study? What population did you sample from? Who/What made up your sample? When and where was the sample obtained? What Method Sampling did you use to select the sample? Give some detail about this.

Do you think you obtained a random sample (did everyone/thing in the population have an equal opportunity to be surveyed)? Explain.

Looking at a yes/no question

For the yes/no questions and answer the following questions:

State the question

Create a pie graph of the yes/no responses.

State the sample proportion of “yes” responses, .

Looking at a numerical questions (Make Sure that you have TWO Quantitative Variables (calorie intake and body weight)

For the each numerical questions answer the following questions:

State the question.

Draw a histogram, box-and-whisker plot,

Calculate the summary statistics (for each data set) Which measure of Central Tendency best describes the data?

Discuss the shape, center, and spread of the distribution of responses to this question.

IV. Scatter Plot

State the two numerical questions. Indicate which variable is x, and which is the dependent variable y. Explain why you assigned the variables in this way.
B. Draw the scatter plot
C. Find the Correlation Coefficient. Do you think that is a Strong, Moderate or Weak Correlation.
D. Find the Line of Best Fit. Draw it on The Scatter Plot.
E. Use the Regression Line to make a Prediction.

 

 

Sort and re-index the bidders so that bitvi > b2w2 > > brawn. Pick winners in this order until one doesn’t fit, and then halt. Return either the solution from the previous step or the highest bidder, whichever has larger social welfare. Call this allocation rule “Method X”. Does a payment rule exist to make Method X DSIC?

None

Imagine you are the captain of a cargo ship and different companies want you to transport their cargo. Each piece of cargo has a certain weight and valuation below. Suppose the ship can carry 17 tons of cargo. Item’s valuations are kept private by the companies but item weights are known publically.
Item/Bidder Valuation Weight
A 10 10
B 9 8
C 6 5
D 4.5 5

Run the Greedy Algorithm and compare that to the Social Welfare Maximizing Allocation.

Determine the price bidder C will pay under the Greedy Algorithm.

Sort and re-index the bidders so that bitvi > b2w2 > >
brawn. Pick winners in this order until one doesn’t fit, and then halt. Return either the solution from the previous step or the highest bidder, whichever has larger social welfare. Call this allocation rule “Method X”. Does a payment rule exist to make Method X DSIC?

For the Greedy Knapsack Heuristic, we are guaranteed to obtain at least 1/2 of the maximum social welfare. Discover the analogous guaranteed social welfare of the allocation rule of Method X or prove that no such guarantee exists. You may assume truthful bidding.

 Does the greedy allocation rule maximize social welfare? Prove the claim or construct an explicit counterexample.Is this a single-parameter environment? Explain fully.

Consider a set M of distinct items. There are n bidders, and each bidder i has a publicly
known subset Ti ⊆ M of items that it wants, and a private valuation vi for getting them. If
bidder i is awarded a set Si of items at a total price of p, then her utility is vixi − p, where xi
is 1 if Si ⊇ Ti and 0 otherwise. Since each item can only be awarded to one bidder, a subset
W of bidders can all receive their desired subsets simultaneously if and only if Ti ∩ Tj = ∅

Is this a single-parameter environment? Explain fully.

(iv) Return W (and give the bidders in W their desired items).
Is this allocation rule monotone (bidder smaller leads to a smaller cost)? If so, find a

Does the greedy allocation rule maximize social welfare? Prove the claim or construct an explicit counterexample.

Can the factor of 12 in the prophet inequality be improved for the special case of i.i.d. distributions, with G1 = G2 = · · · = Gn?

None

Show that the factor of 1
2 in the prophet inequality cannot
be improved: for every constant c > 1
2 , there are distributions

G1, . . . , Gn such that every strategy, threshold or otherwise, has
expected value less than c · Eπ∼G[maxi πi].
(b) Prove that Theorem 6.4 does not hold with 50% replaced by
any larger constant factor.

Can the factor of 12 in the prophet inequality be improved for
the special case of i.i.d. distributions, with G1 = G2 = · · · =
Gn?

Explain how to implement a welfare-maximizing DSIC mecha- nism by invoking this subroutine n + 1 times, where n is the number of participants.

None

Explain how to implement a welfare-maximizing DSIC mecha-
nism by invoking this subroutine n + 1 times, where n is the
number of participants.

Conclude that mechanisms that are ideal in the sense of Theo-
rem 2.4 exist for precisely the families of single-parameter envi-
ronments in which the welfare-maximization problem (given b
as input, compute (4.2)) can be solved in polynomial time.

Prove that the greedy algorithm in the proof of Theo-
rem 4.2 always computes an optimal fractional knapsack solution.
Exercise 4.5 Prove that the three-step greedy knapsack auction al-
location rule in Section 4.2.2 is monotone. Does it remain monotone
with the two optimizations discussed in the footnotes?

Consider a variant of a knapsack auction in which we
have two knapsacks, with known capacities W1 and W2. Feasible
sets of this single-parameter environment now correspond to subsets
S of bidders that can be partitioned into sets S1 and S2 satisfying∑
i∈Sj wi ≤ Wj for j = 1, 2.

Consider the allocation rule that first uses the single-knapsack
greedy allocation rule of Section 4.2.2 to pack the first knapsack,
and then uses it again on the remaining bidders to pack the second
knapsack. Does this algorithm define a monotone allocation rule?
Give either a proof of this fact or an explicit counterexample.

(H) The revelation principle (Theorem 4.3) states that
(direct-revelation) DSIC mechanisms can simulate all other mecha-
nisms with dominant-strategy equilibria. Critique the revelation prin-
ciple from a practical perspective. Name a specific situation where
you might prefer a non-direct-revelation mechanism with a dominant-
strategy equilibrium to the corresponding DSIC mechanism, and ex-
plain your reasoning.
Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781316779309.005
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How did the members of the accounting firms violate the standards of integrity and credibility?

Finance – term paper

Question 1: How did the members of the accounting firms violate the standards of integrity and credibility?
Question 2: Do you believe the new standards that resulted from the Enron scandal to be adequate?
Question 3: Name and explain two aspects of the Sarbanes – Oxley Act of 2002.
Question 4: Ratio Analysis. Using the 2000 Enron 10-K, calculate 2 years of the following liquidity, solvency and profitability ratios. Include your calculations and analysis for these ratios and what they tell you about the company.