1. Find the method of moments estimator for p for the Bernoulli distribution. (see page 78)2. Find the maximum likelihood estimator for p for the Bernoulli distribution. Show your work.3. Find the maximum likelihood estimator for p for the Binomial distribution. Show your work.This is tricky because of our standard notation. Generally, we think of the sample size as n, but in the binomialdistribution we have already defined n as the number of trials from which you count then number of successes X. Let'skeep that definition for n for now, and use the letter m to represent your sample size. Note, that n and m are fixed. Thevalue for p is the one you're trying to find an estimate for.(For clarification - ignore this if it doesn't help. Let's say you're testing lightbulbs in packs of 4 and counting the numberof defective bulbs in the set. In this case n=4 and X can take on any integer from 0 to 4. But now you do this testing 30times in a day, meaning you test 30 packs of 4 lightbulbs. In this case m=30. So at the end of the day, you have 30values, each of which is between 0 and 4. And question 3 is asking you how to use this data to come up with anestimate for p. You need to use the generic variables n, m, p when solving problem 3, but I was hoping that this concreteexample would help put things in context.)

Answered: Image /qna-images/answer/57844913-cd51-4c4f-ac98-4c6856a0bdd7.jpg

Answered: 1. Find the method of moments estimator…

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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Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults found that 8% say their favorite sport is auto racing. You randomly select 600 adults and ask them to name their favorite sport. Complete parts (a) through (d). Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. O A. No, because ng < 5. O B. Yes, because both np25 and ng 25. O C. No, because np <5. (a) Find the probability that the number of people who say auto racing is their favorite sport is at most 56. |(Round to four decimal places as needed.)
Freshmen GPĀS First-semester GPAS for a random selection of freshmen at a large university are shown. Estimate the true mean GPA of the freshman class with 95% confidence. Assume o = 0.62. Round intermediate and final answers to two decimal places. Assume the population is normally distributed. 1.9 2.8 2.2 4.0 1.9 2.8 2.0 2.7 3.9 3.8 3.5 2.7 3.1 3.8 3.0 3.2 2.8 2.7 2.5 1.9 Send data to Excel
Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 55% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below. Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. O A. Yes, because both np 25 and nq 2 5. O B. No, because np < 5. O c. No, because nq < 5. (a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 57, (b) at least 57, and (c) fewer than 57. (Round to four decimal places as needed.) Sketch the graph of the normal distribution with the indicated probability shaded. O A.…
Freshmen GPAS First-semester: GPAS for a random selection of freshmen at a large university are shown below. Estimate mean GPA of the freshman class with 90% confidence. Assume o = 0.62. Use a graphing calculator and round the answers to two decimal places. Assume the population is normally distributed. 1.9 - 3.2 - 2 - 2.9 - 2.7 - 3.3 - 3.5 - 3.8 - 3.9 - 2.7 - 2 - 2.4 - 2 - 2.4 - 2 - 2.9 - 2.5 - 2.7 - 2.8 - 3.2 - 3 - 3.8 - 2.8 - 1.9 - 4 - 2.2
Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 33% name professional football as their favorite sport. You randomly select 11 adults in the region and ask them to name their favorite sport. Complete parts (a) through (d) below (a) Find the probability that the number who name professional football as their favorite sport is exactly 8.
STATISTICAL ANALYSIS (No long explanation needed. Rate will be given and write the complete solutions.) Choose the correct answer. CI on the Mean, Variance Known a. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance increases. b. The probabilities decrease as n increase. As n increase, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases c. The probabilities decrease as n increase. As n increases, the sample variances should deviate the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases d. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance.…
Freshmen GPAs First-semester GPAS for a random selection of freshmen at a large university are shown. Estimate the true mean GPA of the freshman class with 90% confidence. Assume a 0.62. Round Intermediate and final answers to two decimal places. Assume the population is normally distributed. 3.0 3.2 2.8 2.7 2.5 1.9 2.0 2.7 3.8 3.0 2.8 3.3 2.7 2.9 2.0 3.2 1.9 2.8 2.2 4.0 1.9 2.8 2.0 2.7 3.9 Send data to Excel AFW
probability
determine whether the random variable X has a binomial distribution. If it does state the number of trials n. If it does not, explain why not. Twenty students are randomly chosen from a math class of 70 students. Let X be the total number of student absences. Part 1 The random variable -does -does not have a binomial distribution Part 2 Choose the statement that explains why X does not have a binomial distribution, more than one may apply -The Number of trials is not fixed -There are more than two possible outcomes for each trial -The probability of success is not the same for each trial -The trials are not independent -X does not represent the number of successes that occur
Choose the correct distribution to use. The distribution of scores is normal and you know the population standard deviation. Regardless of sample size you use: Select an answer z-score t-score Binomial Geometric Poisson None The original distribution is NOT normal, you know the population standard deviation and your sample size is large (greater than 30), then you use: Select an answer z-score t-score Binomial Geometric Poisson None The original distribution is normal, you do NOT know the population standard deviation. You do have a sample standard deviation. You would then use: Select an answer z-score t-score Binomial Geometric Poisson None The original distribution is NOT normal, you do NOT know the population standard deviation and your sample size is small (less than 30), then you use: Select an answer z-score t-score Binomial Geometric Poisson None The original distribution is discrete, you know the probability of success and you are looking for the probability of getting xx…
Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 52% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below ) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 54, (b) at least 54, and (c) fewer than 54. enter your response here (Round to four decimal places as needed.) .
Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 77% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. Complete parts (a) through (d) below. Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. O A. No, because nq H= 77 H= 77 H=77 The normal distribution cannot be used to approximate the binomial distribution. 63 79 91 63 79 91 63 79 91 (b) Find the probability that the number who have encountered fraudulent charges on their credit cards is at least 79.

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1. Find the method of moments estimator for p for the Bernoulli distribution. (see page 78) 2. Find the maximum likelihood estimator for p for the Bernoulli distribution. Show your work. 3. Find the maximum likelihood estimator for p for the Binomial distribution. Show your work.