Please write down your understanding of binary class linear SVMs. Please cover the following subtopics:

1)The primal form and its dual form for both hard margin and soft margin case;
2) Concept of support vectors
3) Why max-margin is good;
4) Concepts of generalisation/test error;

Light Bulbs

A red light bulb has been flashing forever, according to a Poisson process with rate r. Similarly, a blue bulb has been flashing forever, according to an independent Poisson process with rate b. Let us fix t to be 12 o'clock.

1 What is the expected length of the interval that t belongs to? That is, find the expected length of the interval from the last event before t until the first event after t. Here, an event refers to either bulb flashing.

2 What is the probability that t belongs to an RR interval? (That is, the first event before, as well as the first event after time t, are both red flashes.)

3 What is the probability that between t and t+1, we have exactly two events: a red flash followed by a blue flash?

1. Section 4.4 Contingency Tables & Associations

You Explain it:

1. What is meant by marginal distribution?
2. What is meant by a conditional distribution?
3. Explain why we use the term associationrather than correlationwhen describing the relation between two variables in this section.
4. Explain the idea behind Simpson’s Paradox.

UNAM is known to have a completion rate of 35% with a variance of 6.25%. A Research from
NRCT claims that the variance of UNAM completion rate is not as reported. A sample of 26
students found to have a completion rate of 37% with a variance of 7.29%. (Show all your work
and hypothesis clear steps)

a) Test the Researcher's claims at the 90% level of confidence [14]
b) Construct a 95% confidence interval for the population standard deviation. [6]

Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 14 having a common attribute. The second sample consists of 1900 people with 1370 of them having the same common attribute. Compare the results from a hypothesis test of p 1equalsp 2 ​(with a 0.01 significance​ level) and a 99​% confidence interval estimate of p 1minusp 2. What are the null and alternative hypotheses for the hypothesis​ test? A. Upper H 0​: p 1less than or equalsp 2 Upper H 1​: p 1not equalsp 2 B. Upper H 0​: p 1not equalsp 2 Upper H 1​: p 1equalsp 2 C. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1less thanp 2 D. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1not equalsp 2 E. Upper H 0​: p 1equalsp 2 Upper H 1​: p 1greater thanp 2 F. Upper H 0​: p 1greater than or equalsp 2 Upper H 1​: p 1not equalsp 2 Identify the test statistic. nothing ​(Round to two decimal places as​ needed.) Identify the critical​ value(s). nothing ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.) What is the conclusion based on the hypothesis​ test? The test statistic is ▼ not in in the critical​ region, so ▼ reject fail to reject the null hypothesis. There is ▼ sufficient insufficient evidence to conclude that p 1not equalsp 2. The 99​% confidence interval is nothingless thanleft parenthesis p 1 minus p 2 right parenthesisless than nothing. ​(Round to three decimal places as​ needed.) What is the conclusion based on the confidence​ interval? Since 0 is ▼ not included included in the​ interval, it indicates to ▼ reject fail to reject the null hypothesis. How do the results from the hypothesis test and the confidence interval​ compare? The results are ▼ the same different ​, since the hypothesis test suggests that p 1 ▼ greater than equals less than or equals greater than or equals less than not equals p 2​, and the confidence interval suggests that p 1 ▼ greater than or equals less than greater than less than or equals not equals equals p 2.

What are the mean, median, and mode of a set of data, and how do they differ from each other? What are the different type measures of dispersion? Provide examples of each from your experience.

We consider a randomized experiment, the Tennessee STAR experiment, where students and teachers are randomly assigned to either a small class (15 students) and a regular class (24 students).

We want to estimate the effect of smaller class in primary school and use the following linear model:
Score = β0 + β1ClassSize + Controls + u,
where Score is student’s academic score, Class Size is dummy for small class, and controls includes free lunch status, race, gender, teacher characteristics and so on.

However, you estimate the following model instead:
Score = α0 + α1ClassSize + v

A. Provide the conditions for the OLS estimator for α1 to be unbiased.
B. Provide the Gauss-Markov assumptions for the OLS estimator for α1.
C. Evaluate the sign and the magnitude of bias α1 if teacher’s experience has positive effect on score and more experienced teachers are more likely to be assigned to regular class.
D. Suppose that teachers and students are randomly assigned to either a small class (15 students) or a regular class. Compare α1 to β1.
E. How does the OLS estimator for β1 change as we additionally include parental characteristics as Controls?

An experiment on memory was performed, in which 16 subjects were randomly assigned to one of two groups, called "Sentences" or "Intentional". Each subject was given a list of 50 words. Subjects in the "Sentences" group were told to form multiple sentences, each using at least two words from the list, and to keep forming sentences until all the words were used at least once. Subjects in the "Intentional" group were told to spend five minutes memorizing as many of the 50 words as possible. Subjects from both groups were then asked to write down as many words from their lists as they could recall. The data are in the table below.

Enter this data into JMP in "long form" (e.g. each column should be a variable and each row should be an observation).
IMPORTANT: to format this data correctly, you need to think about what your two variables are (they are not 'Sentences' and 'Intentional'). You may want to look at how the deflategate data are formatted if you have trouble figuring this out.

We are interested in determining if there is a significant difference in the average number of words recalled for subjects in the "sentences" group vs. subjects in the "intentional" group, using α = 0.05. Use JMP to answer the questions below, and round all answers to three decimal places.

a. The appropriate null/alternative hypothesis pair for this study is:
(you have two attempts at this question)

H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional ≠ 0Ho: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional < 0    H₀: μ_d = 0 ; H_A: μ_d ≠ 0H₀: μ_sentences - μ_intentional = 0 ; H_A: μ_sentences - μ_intentional > 0H₀: μ_d = 0 ; H_A: μ_d < 0H₀: μ_d = 0 ; H_A: μ_d > 0

b. Enter the values for the following statistics:

x_sentences = (No Response)
s_sentences = (No Response)
x_intentional = (No Response)
s_intentional = (No Response)
(x_sentences - x_intentional) = (No Response)
standard error of (x_sentences - x_intentional) = (No Response) (you have to use 'Analyze / Fit Y by X' to get JMP to calculate this)
test statistic: t = (No Response)
p-value = (No Response)

c. Report the 95% confidence interval JMP gives for μ_sentences - μ_intentional

Lower bound = (No Response)
Upper bound = (No Response)

d. From these results, our statistical conclusion should be:
(You have two attempts at this question.)

The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and zero is inside the confidence intervalThe means for "sentences" and "intentional" differ significantly, because the p-value is less than α and zero is outside the confidence interval    The means for "sentences" and "intentional" differ significantly, because the p-value is less than α and -2.625 is inside the confidence intervalThe means for "sentences" and "intentional" differ significantly, because the p-value is less than α and -2.625 is outside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and zero is inside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and zero is outside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and -2.625 is inside the confidence intervalThe means for "sentences" and "intentional" do not differ significantly, because the p-value is greater than α and -2.625 is outside the confidence interval

Another coefficient mentioned in this week's readings is the coefficient of determination, r^2. What information do we obtain from this coefficient?

In a random sample of​ males, it was found that 23 write with their left hands and 217 do not. In a random sample of​ females, it was found that 66 write with their left hands and 450 do not. Use a 0.01 significance level to test the claim that the rate of​ left-handedness among males is less than that among females. Complete parts​ (a) through​ (c) below. a. Test the claim using a hypothesis test. Identify the test statistic. Identify the​ P-value. What is the conclusion based on the hypothesis​ test? b. Test the claim by constructing an appropriate confidence interval. What is the conclusion based on the confidence​ interval? c. Based on the​ results, is the rate of​ left-handedness among males less than the rate of​ left-handedness among​ females?

Geoff is running a carnival game. He has 15 marbles in a bag: there are 4 green marbles, 7 red marbles and 4 yellow marbles. To play a round of the game, a player randomly takes out 2 marbles (without replacement) from the bag. Green marbles win 5 points, red marbles win 1 point and yellow marbles lose 2 points.

Let X be the random variable that describes the number of points won by a player playing a single round of Geoff's marble game. Find the probability distribution for X. Give values for X as whole numbers and probabilities as decimal values to 3 decimal places. Enter the values for X in ascending order (lowest to highest) from left to right in the table.

A cross-sectional survey was conducted on adults (³20 years of age) residing in the Khairpur district in Sindh province of Pakistan. One objective of the survey was to evaluate the relationship of social economic position with under- and overweight. The following table gives the frequency counts for the number of participants in socioeconomic status (low, median, high) and BMI for a random sample of 1000 participants.

1) what is the probability that a randomly selected participant is both Normal (A) and falls in the Median social economic class (B)?

- step-by-step explanation on excel if possible and/or formula write out

2) what is th probability that a randomly selected participant is either Overweight/obese (A) or falls in the low level social economic class (B)?

- step-by-step explanation on excel if possible and/or formula write out

3) Suppose a randomly selected participant is form the Low Social Economic Class (A). Given this knowledge what is the probability that this person is overweight (B).

- step-by-step explanation on excel if possible and/or formula write out

4) Is being overweight (A) independent of social economic class? Consider the case of whether or not a randomly selected participant falls in the Low Social Economic Class (B) to answer this question?

- step-by-step explanation on excel if possible and/or formula write out

You wish to test the following claim ( H a ) at a significance level of α = 0.005 . H o : p = 0.71 H a : p ≠ 0.71 You obtain a sample of size n = 293 in which there are 187 successful observations. Determine the test statistic formula for this test. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =