Let our experiment consist of rolling two four-sided dice. So our sample space \( S \) consists of 16 objects in the form of \((a,b)\) where \( a \) is the result of the first die and \( b \) is the result of the second die. Notice that the object \((1,3) \neq (3,1)\) for example.1. Consider events \( A = \) “The sum of the roll is 5” and \( B = \) “The distance between \( a \) and \( b \) is 1”. Write both of these events in set notation using \(\{ \}\) brackets. (2pts)2. Write \( A \text{ and } B \) and \( A \text{ or } B \) as sets. (Hint: \( A \text{ and } B \) has 2 objects, \( A \text{ or } B \) has 8 objects) (2pts)3. Using the \(\frac{f}{N}\) method, find \( P(A) \), \( P(B) \), \( P(A \text{ and } B) \), and \( P(A \text{ or } B) \). (4pts)4. Use the “General Addition Rule” to find \( P(A \text{ or } B) \), show your work. (2pts)

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Answered: Let our experiment consist of rolling…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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please explain each step clearly/why you did it this way. Neat handwriting and boxed answers, please. Thank you
An ice cream parlor serves 10 flavors of ice cream. Carrie and Jimmy each randomly and independently choose 3 out of those 10 flavors. Use the method of indicators to find the expected number of flavors chosen by both Carrie and Jimmy and simplify your final answer**** ****Each person has to choose 3 different flavors (Vanilla- Vanilla-Chocolate is not ok) but their flavors are allowed to overlap (Chocolate-Vanilla-Strawberry for Carrie and Chocolate- Blueberry-Mint for Jimmy is ok). The order of flavors doesn’t matter.
This semester, we have talked about creating random samples as well as desirable qualities of random samples. Other than randomness, one quality of random samples that we have talked about is representation. Using your knowledge of that concept, consider this problem. At a college, 29% of the students are in their first year, 27% are in their second year, 25% in their third, and 19% in their fourth. You take a survey of students and when you classify them by year of study, you have 49, 70, 56, and 25 students in their first, second, third, and fourth years respectively. The table below highlights this information. Year of School First Second Third Fourth Total College Percents Sample Counts Expected Counts 27% 70 25% 56 29% 19% 49 25 200 58 54 50 38 Under the assumption that we think the college enrollment percentages should match our sample, and that therefore our sample represents the college: a) What would the critical value be? (use a = 0.05) b) Find the test statistic to test (c)…
2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:
As part of a statistics project, a teacher brings a bag of marbles containing 700 white marbles and 300 red marbles. She asks her students to determine how many red marbles are in the bag without counting them.A student randomly draws 100 marbles from the bag. Of the 100 marbles, 33 are red.The target population consists of The 100 marbles drawn by the student The 1000 marbles in the bag None of the above The 33 red marbles drawn by the student The 300 red marbles in the bag The sample consists of The 1000 marbles in the bag The 100 marbles drawn by the student The 33 red marbles drawn by the student None of the above The 300 red marbles in the bag Based on the sample, the student would estimate that ------ marbles in the bag were red.
Here is a sample of amounts of weight change (kg) of college students in their freshman year: 13, 7, -3, -5, where -5 represents a loss of 5 kg and positive values represent weight gained. Here are ten bootstrap samples: {13, 13, 13, -3), (13, -5, -3, 13}, {13, 5, 7, 3), (7, 5, 3, 13), {-3, -3, -3, 7}, {7, 5, 7, 5), (13, 7, 5, 3}, {-5, 7, 5, 7), {-5, -3, -5, 7}, {7, 13, 13, 13). Complete parts (a) and (b) below. a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the mean weight change for the population. (Round to one decimal place as needed.)
What is the value of ΣX for the scores 2, 5, 3?

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