A chord of a circle of radius a is drawn parallel to a givenstraight line, all distances from the centre of the circle being equally likely.26.1Ta and that theShow that the expected value of the length of the chord isvariance of the length. is3aа(32 – 3T). Also show that the chance is1that12.:2the length will exceed the length of the side of an equilateral triangleinscribed in the circle

Answered: Image /qna-images/answer/42fdc8af-1210-4be6-bb37-a7ca410bcfc7.jpg

Answered: A chord of a circle of radius a is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Using a long rod that has length m, you are goingto lay out a square plot in which the length of eachside is m. Thus the area of the plot will be m2.However, you do not know the value of m, soyou decide to make n independent measurementsX1, X2,... Xn of the length. Assume that each Xihas mean m (unbiased measurements) and variance s2.a. Show that X2 is not an unbiased estimatorfor m2. [Hint: For any rv Y, E(Y2) ¼V(Y) + [E(Y)]2. Apply this with Y ¼ X.]b. For what value of k is the estimator X2 - kS2unbiased for m2? [Hint: Compute E(X2 - kS2).]
Please don't provide hand written solution
Use the t-distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distributions are relatively normal. Test Ho : HA = Ha VS H. : HA # Hg using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation of 14. (a) Give the test statistic and thep-value. Round your answer for the test statistic to two decimal places and your answer for the p- value to three decimal places. test statistic = p-value = eTextbook and Media (b) What is the conclusion of the test? Test at a 10% level. O Reject Ho. O Do not reject Ho. eTextbook and Media
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.4 parts/million (ppm). A researcher believes that the current ozone level is not at the normal level. The mean of 1090 samples is 4.3 ppm. Assume the variance is known to be 1.44. Does the data support the claim at the 0.05 level? Step 1 of 5: Enter the hypotheses: Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Enter the decision rule. Step 5 of 5: Enter the conclusion.
Question 8. This question is similar to Exercise 11 on page 363 of your textbook. Let t be a t-random variable. P(ta) = 0.05 and 65 degrees of freedom. Use Excel function =t.inv to find a. ii. Use Excel function =t.dist to find P(t 2.16) with df =23 This is a fill-in-blank question. Do not show your work. Write your answer with the format of #.###, #.####, #.####. The first number is for (i), the second number is for (ii), and so on.
49 of 2. CO 60 8 7. Fill in the table below: FiLl in the differences of each data value from the mean, then the squared lifferences. 2. I'– 1) 5. 3. -5 9. 14 7. 6. -1 25 8. 1. 49. 3) Calculate the sample standard deviation (s). 12 a) ENG 2/1 dy ins prt sc f12 delete home + backspace unu lock
A random sample of size 225 is taken from a population with a mean of 10 and variance 4. Find the probability that the sample mean is greater than 9.8 but less than 10.2.
As a bonus assignment a former student checked if your professor gave a statisticallysignificant difference in grades between his male and female students. She based herstudy based on grades assigned in intermediate Econ courses (Econ 303, 305 and 317)and her sample included nm = 485 male students and nf = 264 female students. Theaverage grades received were xm = 84.6 and xf = 85.8 The population standad deviation were σ m = 12.0 and σ f = 11.4 8. From the same extra-credit study as in question 7 see above, this former student found that the proportion of female students in principle courses (Econ 203, 205) was ?̅? = 0.380, while the proportion of female students in intermediate courses (Econ 303, 305, 317) was ?̅? = 0.352. The principle courses sample size was np = 782, while the intermediate courses sample size was ni = 749. Test the hypothesis that female students are less in intermediate courses using a 90% confidence level and the p-value approach.
Suppose that weights of college mathematics textbooks in the United States are normally distributed with mean µ = 2.25 lbs and variance σ2 = 0.2025 lbs. Find the weight that corresponds to Q3 and interpret this measure of position in the context of the problem.
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The mean shopping time, µ, spent by customers at the supermarkets has been reported to be 40 minutes, but executives hire a statistical consultant and ask her to determine whether it can be concluded that u is greater than 40 minutes. To perform her statistical test, the consultant collects a random sample of shopping times at the supermarkets. She computes the mean of these times to be 44 minutes and the standard deviation of the times to be 15 minutes. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? Hiµ is ? H: p is ? In the context of this test, what is a Type II error? A Type II error is ? fact, u is ? the hypothesis that u is when, in Suppose that the consultant decides not to reject the null hypothesis. What sort of error might she be making?
Suppose that having a widow's peak was a dominant trait (W) compared to not having a widow's peak (w). In a sample size of 30 students, 15 were observed to have a widow's peak and 15 did not have a widow's peak. The expected frequency of a widow's peak is 75% chance of getting it and a 25% chance of not getting it. Perform a chi square analysis to see if the data above agrees with the predicted outcome.

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS