Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.6. Assume that the trials are independent a. Find the probability that the first successful alignment requires trials four trials at the maximum b. Calculate the mean of x c. Calculate the variance of x

Suppose that the probability of a successful optical alignment in the assembly of an optical data storage product is 0.6. Assume that the trials are independent a. Find the probability that the first successful alignment requires trials four trials at the maximum b. Calculate the mean of x c. Calculate the variance of x

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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31. Explain minimum variance unbiased estimation with example. Let yı, y2, ..., Yn be a random sample from a population with mean µ and variance oʻ. Show that among all linear combinations Eay, which are i = 1 unbiased estimators of µ, thè sample mean y has the smallest variance.
Many properties of the fabric used in different textiles, such as sheets and clothing, are influenced by whether the diameter of yarn used in the creation of the textile is consistent. Therefore, various methods can be used to measure the diameter of yarn at specified intervals, such as every 2mm, to determine the consistency of the diameter. These measurements are normally distributed. Suppose that one textile manufacturer will not use any yarn in which the variance of the diameters is greater than 0.0009mm. In order to ensure that the yarn is usable, the diameter of a length of yarn is measured at 100 random intervals. The variance of those measurements is found to be 0.001119mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.025 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
Let y1, y2, and y3 be a random sample from a poisson distribution with mean λ. Suppose that the following are estimators of λ: λhat1 = ȳ λhat2 = y1/n 1. Which estimator is/are biased or unbiased. Show your solution and if biased, compute for the bias. 2. Find which estimator has the largest variance.
Many properties of the fabric used in different textiles, such as sheets and clothing, are influenced by whether the diameter of yarn used in the creation of the textile is consistent. Therefore, various methods can be used to measure the diameter of yarn at specified intervals, such as every 2mm, to determine the consistency of the diameter. These measurements are normally distributed. Suppose that one textile manufacturer will not use any yarn in which the variance of the diameters is greater than 0.0009mm. In order to ensure that the yarn is usable, the diameter of a length of yarn is measured at 100 random intervals. The variance of those measurements is found to be 0.001148mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.10 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
The probability mass function for the number x of coding errors found in 1000 randomly selected lines of computer code is given by x: 0, 1, 2, 3, 4 p(x): .08, .15, .45, .27, .05 a. Calculate the mean number of coding errors for all such blocks of 1000 lines of code. b. Calculate the variance and standard deviation of x.
2) Let G and H be two independent unbiased estimators of 0. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately o² = 47.1. However, a random sample of 17 colleges and universities in Kansas showed that x has a sample variance s² = 82.7. Use a 5% level of significance 1 test the claim that the variance for colleges and universities in Kansas is greater than 47.1. (a) What is the level of significance? State the null and alternate hypotheses. Ho: o²=47.1; H: o> 47.1 Ho: o²=47.1; H: o2 0.100 0.050 a, we fail to reject the null hypothesis. Since the P-value > x, we reject the null hypothesis. Since the P-values ∞, we reject the null hypothesis. Since the P-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries…
The built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x<-rock$shape. Assume that the n area measurements x=(x1, x2,...,xn) are a random sample from a population with true unknown mean ? and true unknown variance ?2. Remember, let x be defined by x<-rock$shape.
The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Jelly Belly Candy Company is testing two machines that use different technologies to fill three pound bags of jelly beans. The following tables contain a sample of data on the weights of bags (in pounds) filled by each machine. Machine 1 Machine 2 Ho: 01 2 Ho: 01 State the null and alternative hypotheses. 2 2 Ha: 01 Ha: 01 2.95 3.45 3.50 3.75 3.48 3.26 3.33 2 Ha: 01 ≤0₂ 3.16 3.20 3.22 3.38 3.90 3.36 3.25 2 3.20 2 3.12 Ho: 01 Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? = 2 Ho: 01 #0 2 02 = 2 2 02 02 2 2 2 ≤02 3.20 2 2 H₂: 01 > 02 3.28 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.22 3.30 3.34 3.28 3.29 3.25 3.30 3.27 3.38 3.34…
Many properties of the fabric used in different textiles, such as sheets and clothing, are influenced by whether the diameter of yarn used in the creation of the textile is consistent. Therefore, various methods can be used to measure the diameter of yarn at specified intervals, such as every 2mm, to determine the consistency of the diameter. These measurements are normally distributed. Suppose that one textile manufacturer will not use any yarn in which the variance of the diameters is greater than 0.0009mm. In order to ensure that the yarn is usable, the diameter of a length of yarn is measured at 400 random intervals. The variance of those measurements is found to be 0.000992mm. Does this evidence provide support that the batch of yarn is unusable by the manufacturer? Use a 0.005 level of significance. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
With unit variance; the random variable Y is related to the random variable X by a linear relationship. A. Calculate the minimum error power when X and Y are fully correlated. B. Calculate the minimum error power when X and Y are not related at all.