Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Business Mathematics II Homework 8 for Math 115b, Sections: 18 Instructor: Ratnayaka Due Date: by Team: (Number) We, the undersigned, affirm that each of us participated fully and equally in the completion of this assignment and that the work contained herein is original. Furthermore, we acknowledge that sanctions will be imposed jointly if any part of this work is found to violate the Student Code of Conduct, the Code of Academic Integrity, or the policies and procedures established for this course. ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature ______________________________ Name (printed) ______________________________ Signature Problem 1 Use Variance.xls to compute 10 samples, each of size n 3 , for both X and Y. (i) Compute the average of the 10 sample errors for the samples from X and (ii) do the same for the 10 sample errors for the samples from Y. Problem 2 Let X be a random variable whose p.m.f. is given below. x f X (x) 1 0.2 0 0.4 1 0.2 2 0.1 4 0.1 Use Excel to compute V ( X ) and X . Problem 3 Let X be a finite random variable, which can assume only the values 1, 2, 5, 10, and 100. If each of these values is equally likely to occur use Excel or a calculator to compute V ( X ) and X . Problem 4 Let X be a binomial random variable with n 6 and p 0.3 . In an Excel file, create a table that lists the possible values of X, and use BINOMDIST to list the probabilities of these values. (See Finite Random Variables in Distributions for a discussion of BINOMDIST.) Use the method of Example 2 and an Excel file that is similar to Binomial 2.xls to compute the variance and standard deviation of X. Problem 5 Let X be a binomial random variable with n 6 and p 0.3 . Use the special formulas for mean and variance that apply only to binomial random variables, to compute the mean, variance, and standard deviation of X. Problem 6 Let W be the working lifetime (in years) of the microchip in your new digital watch. The manufacturer claims that W has an exponential distribution with mean lifetime of 5 years. Use Excel and the method of Example 4 to compute the variance and standard deviation of W. Problem 7 Let X be the continuous uniform random variable on [0,10] . Compute the mean, variance, and standard deviation of X. Problem 8 Let X be the continuous random variable with p.d.f. if x 0 0 f X ( x) 2 2x3 if 0 x. 6 x e Use Integrating.xls to compute V ( X ) and X . Problem 9 Let X be the continuous random variable that is uniform on [0,8] , and let S be the standardization of X. Use the method of Example 7 to compute P (1 S 1) . Problem 10 Let X be the exponential random variable with parameter 3 . Recall that both the mean and standard deviation of X are equal to three. Let S be the standardization of X. Compute P ( S 1) . First express P ( S 1) in terms of a probability for X, then use the formula for the cumulative distribution function of X to finish the exercise. See Continuous Random Variables in Distributions.) Problem 11 Use Excel and the method of Example 8 to compute the mean, variance, and standard deviation of the following random sample for the values of a random variable X. 10.2, 6.2, 10.8, 10.2, 12.1, 7.7, 10.7, 6.4, 13.1 Problem 12 Use VAR and STDEV to compute s 2 and s for the sample in Exercise 17. Problem 13 Let X be a random variable with a mean of 75 and a standard deviation of 6. Let x be the sample mean for random samples of size n 20 . Compute the expected value, variance, and standard deviation of x . * Problem 14 * Let R be the random variable that gives the error in a signal from your team’s data. Compute your sample standard deviation, s, as an assumed value for the standard deviation, R , of R.