Tag: Mathematics

1. To test the understanding and application of Mathematical concepts learning.

2. To test the calculation skills and Mathematical modelling ability of the learner.

3. To test the knowledge acquired by the learners on using statistical test and ability to infer
on the outcomes.

It is 2 questions on engineering statics as you see in the pictures. Please note that first has 5 parts (a,b,c,d,e) and second one has 3 parts(a,b,c). Please if you are not sure about the questions and their answers do not take the task. I only need the direct answer no need for explanation.

Type I and Type II errors

Balancing the Risks of Errors in Hypothesis Testing
The U.S. FDA is responsible for approving new drugs. Many consumer groups feel that the approval process is too easy and, therefore, too many drugs are approved that are later found to be unsafe. On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. This is from an article in the Wall Street Journal. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe.
a) Explain the risks of committing a Type 1 or Type 2 error.
b) Which type of error is the consumer group trying to avoid?
c) Which type of error is the industry lobbyists trying to avoid?
d) How would it be possible to lower the chances of both Type 1 and 2 errors?
Think about the recent vaccinations developed for Covid in record time. Do you recall reading about the items above and are they important?

Six Sigmas

Many of you will have heard of Six Sigma management. What you may not realize is that the etymology of the term Six Sigma is rooted in statistics. As you should have seen by now, statisticians use the Greek letter sigma (σ) to denote a standard deviation. So when these Six Sigma people start talking about “six sigma processes,” what they mean is that they want to have processes where there are (at least) six standard deviations between the mean and what would be determined to be a failure. For example, you may be examining the output of a factory that makes airline grade aluminum. The average tensile strength of each piece is 65 ksi, and you view a particular output as a failure if the tensile strength is anything less than 64 ksi. If the standard deviation is less than .166, then the process is six sigma. The odds of a failure within a six sigma process are 3.4 in a million, which corresponds to the 99.9997% confidence level. When we are doing statistics, we usually use the 95% confidence level, which is roughly 2 sigmas.
In the case of the tensile strength of airline grade aluminum, 6 sigmas is probably a good level to be at—catastrophic failure on an airplane could open you up to lawsuits worth billions of dollars. But there are some other processes that you probably don’t need to be so certain about getting acceptable products from. Give some examples from your own business life of random processes that are likely to be normally distributed, and say how many sigmas you think the process should be at.

Analysis of Variance (ANOVA) at the Workplace

Web site: http://www.statisticshowto.com/anova/
Case scenario.
• At the workplace, you are the research team leader.
• The Boss wants your team to conduct a study with three or more groups to solve a problem.
• Since there are many workplace problems, you must select the problem for the study.
• In six-sentences or more, describe the study with three or more groups.
• In the paragraph, include information for the following questions:
• What is the problem and why?
• What would be the treatment/experimental groups and what would be the control group?
• What would be the Independent variable and the dependent variable for the study and why?
• What would be the null and alternative hypotheses for the study?
• What would be the alpha level and why?

Hint: The chart is taken from https://ourworldindata.org/technological-progress.

From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore’s Law, what would you predict the number of transistors per IC to be in 2040?

In some applications, the variable being studied increases so quickly (“exponentially”) that a regular graph isn’t informative. There, a regular graph would show data close to 0 and then a sudden spike at the very end. Instead, for these applications, we often use logarithmic scales. We replace the y-axis tick marks of 1, 2, 3, 4, etc. with y-axis tick marks of 101 = 10, 102 = 100, 103 = 1000, 104 = 10000, etc. In other words, the logarithms of the new tick marks are equally spaced.

Technology is one area where progress is extraordinarily rapid. Moore’s Law states that the progress of technology (measured in different ways) doubles every 2 years. A common example counts the number of transitors per integrated circuit. A regular y-axis scale is appropriate when a trend is linear, i.e. 100 transistors, 200 transistors, 300 transistors, 400 transistors, etc. However, technology actually increased at a much quicker pace such as 100 transistors,.1,000 transistors, 10,000 transistors, 100,000 transistors, etc.

The following is a plot of the number of transistors per integrated circuit over the period 1971 – 2008 taken from https://ourworldindata.org/technological-progress (that site contains a lot of data, not just for technology). At first, this graph seems to show a steady progression until you look carefully at the y-axis … it’s not linear. From the graph, it seems that from 1971 to 1981 the number of transistors went from about 1,000 to 40,000. Moore’s Law predicts that in 10 years, it would double 5 times, i.e. go from 1,000 to 32,000, and the actual values (using very rough estimates) seem to support this.

The following is the same plot but with the common logarithm of the y-axis shown. You can see that log(y) goes up uniformly.

Questions to be answered in your Brightspace Discussion:

Part a: The number of transistors per IC in 1972 seems to be about 4,000 (a rough estimate by eye). Using this estimate and Moore’s Law, what would you predict the number of transistors per IC to be 20 years later, in 1992?

Prediction =

Part b: From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore’s Law, what would you predict the number of transistors per IC to be in 2040?

Part c: Do you think that your prediction in Part b is believable? Why or why not?

This is all the material that you will need. Please let me know if you have any questions.

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THE DUE DATE IS NOT IN 13 HOURS
I JUST MADE IT 13 HOURS TO PREVENT AUTOMATCH. WE START IN 2 HOUR

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please accept if you are 100% confident. any low grade will result in a bad review and REFUND request

PLEASE READ THE QUESTION TITLE CAREFULLY

THE DUE DATE IS NOT IN 13 HOURS

PLEASE READ THE QUESTION TITLE CAREFULLY

THE DUE DATE IS NOT IN 13 HOURS

PLEASE READ THE QUESTION TITLE CAREFULLY

THE DUE DATE IS NOT IN 13 HOURS

PLEASE READ THE QUESTION TITLE CAREFULLY

THE DUE DATE IS NOT IN 13 HOURS

PLEASE READ THE QUESTION TITLE CAREFULLY

THE DUE DATE IS NOT IN 13 HOURS

PLEASE READ THE QUESTION TITLE CAREFULLY

THE DUE DATE IS NOT IN 13 HOURS

Use the results from the Online Learning Readiness Questionnaire to answer these questions.

Goal: To evaluate your readiness to succeed in this course and make plans to overcome anything that might block your progress.

Self Direction

1. What was the advice given to you in this section?
2. How will you use this advice to succeed in Stat 95?

Learning Preferences

1. What was the advice given to you in this section?
2. How will you use this advice to succeed in Stat 95?

Study Habits

1. What was the advice given to you in this section?
2. How will you use this advice to succeed in Stat 95?

Technology Skills

1. What was the advice given to you in this section?
2. How will you use this advice to succeed in Stat 95?

Computer Equipment Capabilities

1. What was the advice given to you in this section?
2. How will you use this advice to succeed in Stat 95?

When reviewing the advice from the Online Readiness Questionnaire, you should make use of all of the tools and resources that they recommend, except those that are specifically for UNC students, such as the UNC ITS Help Desk. If you have technical issues, you should contact the SJSU Help Desk (Links to an external site.) (http://its.sjsu.edu/support/ (Links to an external site.)).

The handouts page can be found here: http://learningcenter.unc.edu/handouts/ (Links to an external site.)

Instructions for uploading papers to CANVAS

1. Return to the Assignments page in Canvas (https://sjsu.instructure.com/)
2. Click the “Submit Assignment” link to the right of the “Reflecting on your preparedness”
3. Click on “Choose File,” find, and select the document on your computer with your written answers.
4. Click “Open.”
5. Click “Submit Assignments” when all the files to be uploaded have been selected.
6. You should see that the submission status in the upper right side of the page indicates “Turned In!”

Search the Troy library’s catalog and find a journal article that uses statistics to address a social science topic. Once you click the link, enter a search term. For example, you might try policing, gender, bullying, inequality, or wealth. You can search for any topic you want to though. Once you have your results, check the checkboxes on the left hand side of your page to show only articles, full-text, and within the last 5 years. Share the link to an interesting article and briefly describe it. I know that some of the statistical methods used will be beyond what we’ve done in here, so you don’t have to go into great detail. Just tell us enough to know whether or not we want to read the article for ourselves. What were the main findings?

Problem 1. 8 points

Suppose that x1; x2; x3; x4, is a sample drawn from the uniform distribution

f(x; ) :=

(

1

if x 2 [1; 1 + ];

0 otherwise;

where is an unknown parameter. Let y1; y2; y3; y4 be the associated order statistics.

(a) [2 points] Find an expression for the joint likelihood function f(x1; x2; x3; x4; ).

(b) [2 points] Is y2 a sucient statistic for ? Give a brief explanation of your answer.

(c) [2 points] Now suppose that x1 = 5; x2 = 3; x3 = 4; x4 = 2. Find the maximum likelihood

estimate of .

(d) [2 points] Using the values from part (c), nd the method of moments estimate for .

(Hint: there is only one parameter so you only need to compute the rst moment).

Problem 2. 4 points

Suppose that X1; : : :Xn are i.i.d. random variables with probability density function

f(x; ) =

(

e x if x 0

0 otherwise.

(a) [2 points] Give an expression for the joint likelihood function f(x1; : : : ; xn; ).

(b) [2 points] Show that the sample mean is a sucient statistic for .

Problem 3. 3 points

Suppose you collect a sequence of data points (x1; y1); : : : ; (xn; yn) and you use least squares

regression to nd the values of 0 and 1 so that the line y = 1x + 0 gives the best match

to the data. Show that if the data points already lie on a line y = mx + b i.e. (yi = mxi + b

for i = 1; : : : ; n), then least squares regression chooses the parameters 0 = b and 1 = m.

Problem 4. 10 points

Suppose you are playing a random game that has three possible outcomes WIN, LOSE or

DRAW. The probability of winning the game is an unknown parameter 2 [0; 1], losing and

drawing have equal probability 1

2(1 ). Suppose you have a prior on the data that is given

by h() = 2.

(a) [3 points] Suppose that it costs $5 to play the game, you get $15 dollars if you win,

nothing if you draw, and you have to pay an additional $2 if you lose. Based on the prior

distribution would you play the game? Explain.

(b) [3 points] Now suppose you observe the following sequence of (independent) game out-

comes: WIN, LOSE, DRAW, DRAW, WIN, LOSE, WIN, LOSE, DRAW, DRAW. Give

an expression for the posterior distribution of .

(c) [3 points] Based on the posterior distribution would you play the game?

(d) [1 point] Would your answer to part (c) change if you had observed the following sequence

of (independent) game outcomes instead: WIN, LOSE, LOSE, LOSE, WIN, LOSE, WIN,

LOSE, LOSE, LOSE. Give a brief explanation of your reasoning.

(2.5)Explain how you determine numbers in regions II, IV, VI when constructing a Venn diagram.

(3.1) What is a statement?  What is a  compound statement?

(3.1) Provide the table of 5  logical connectives with formal name, symbol, read and symbolic form.

(3.2) Describe the 5-step procedure  to construct truth table.

(3.2) Provide truth table for negation, conjunction and disjunction.