Maryland, CMSC 12
Excerpt: ... standard deviation equal to 0.1 for all 6 components (cf. slide 17 on lecture about Tracking and Kalman filtering). c.) Write the state equation, assuming Gaussian noise with a standard deviation equal to 0.1 for each of the 6 state components. d.) Write the measurement equation, assuming Gaussian noise with standard deviation equal to 2 for each of the 3 measurement components. e.) Write a Matlab Kalman filter function to compute a position estimate of the missile (defined by 3 components) at each time step. f.) Run the Kalman filter (you can use an initial position estimate of (0, 0, 0), an initial velocity estimate of (0, 0, 0), and an initial covariance matrix for the prediction error equal to an identity matrix). Plot the estimates for the missile coordinates on the same figure as the measurements used in (a). 3. Read Chapter 19.4 of the book by Forsyth and Ponce on the condensation or particle filter (It is available on the web at http:/www.cs.berkeley.edu/~daf/book3draft/tracking.pdf) 4. After you fi ...
Georgia Tech, CEE 3770
Excerpt: ... e you want to test a randomly selected sample of n water specimens and estimate the mean daily rate of pollution produced by the mining operation. If you want 95% condence interval estimate of width 2 milligrams, how many specimens you need to sample? Assume prior knowledge indicates that pollution readings in water samples taken during a day are approximately normally distributed with a standard deviation equal to 5 milligrams. Solution: 95% half width = 1 = z/2 2 n 52 1 = z0.025 n 2 2 n = 1.96 5 n = 1.962 52 n = 96 1 3. The average speed of vehicles on a highway is being studied. (a) Suppose that observations on 50 vehicles yielded a sample mean of 65 mph. Assume that the standard deviation of vehicle speed is known to be 6 mph. Determine two-sided 99% condence intervals of the mean speed. Solution: 99%CI = X z/2 2 n 62 = 65 z0.005 50 6 = 65 2.58 50 = 65 2.189 (b) In part (a), how many additional vehicles speed should be observed such that the mean speed can be es ...
SUNY Stony Brook, AMS 310.01
Excerpt: ... e told that the probability of a defective equals 0.2. (a) Write an expression for the exact probability that in a sample of 100 we observe less than 15% defective. (b) Find the approximate probability that in a sample of n=100 we observe less than 15% defective. (c) For the sample of n=100, find the value of c such that Pr(X c) 0.01. 3. System breakdowns are distributed, according to a Poisson law at an average of 0.5 per hour. (a) What is the probability that the time between system breakdowns is less than 1.5 hours? (b) We do a study to see if this assumption of 0.5 per hour is correct by recording the time between system breakdowns for 100 days. Use the Central limit theorem to determine the approximate probability that the sample mean will be less than 1.5 hour. 4. Suppose that the weight of people getting on the elevator has mean 150 lb and standard deviation equal to 30 lb. and is normally distributed. The elevator contains a sign saying that "No more than 8 people Allowed on this Elevator". (a) Su ...
Wisc La Crosse, MATH 145
Excerpt: ... Math 145 - Elementary Statistics Chapter 7 Exercises July 12, 2007 1. A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation equal to 1.5 deciliters. A random sample of 36 drinks had an average content of 22.5 deciliters. a. Construct a 95% confidence interval estimate for the mean of all drinks dispensed by this machine. b. Give a practical interpretation for the interval estimate you obtained in part (a). c. Determine how large a sample is needed if we wish to be 95% confident that our estimate will be within 0.1 deciliters of the true mean? d. Construct a 99% confidence interval estimate for the mean of all drinks dispensed by this machine. Interpret your answer. e. Determine how large a sample is needed if we wish to be 99% confident that our estimate will be within 0.1 deciliters of the true mean? 2. The contents of 10 similar containers of a commercial soap are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9 ...
Wisc La Crosse, MATH 145
Excerpt: ... Math 145 - Elementary Statistics Chapter 7 Exercises March 26, 2008 1. A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation equal to 1.5 deciliters. A random sample of 36 drinks had an average content of 22.5 deciliters. a. Construct a 95% confidence interval estimate for the mean of all drinks dispensed by this machine. b. Give a practical interpretation for the interval estimate you obtained in part (a). c. Determine how large a sample is needed if we wish to be 95% confident that our estimate will be within 0.1 deciliters of the true mean? d. Construct a 99% confidence interval estimate for the mean of all drinks dispensed by this machine. Interpret your answer. e. Determine how large a sample is needed if we wish to be 99% confident that our estimate will be within 0.1 deciliters of the true mean? 2. The contents of 10 similar containers of a commercial soap are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and ...
Wisc La Crosse, MATH 145
Excerpt: ... Math 145 - Elementary Statistics Chapter 7 Exercises October 22, 2008 1. A soft-drink machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation equal to 1.5 deciliters. A random sample of 36 drinks had an average content of 22.5 deciliters. a. Construct a 95% confidence interval estimate for the mean of all drinks dispensed by this machine. b. Give a practical interpretation for the interval estimate you obtained in part (a). c. Determine how large a sample is needed if we wish to be 95% confident that our estimate will be within 0.1 deciliters of the true mean? d. Construct a 99% confidence interval estimate for the mean of all drinks dispensed by this machine. Interpret your answer. e. Determine how large a sample is needed if we wish to be 99% confident that our estimate will be within 0.1 deciliters of the true mean? 2. The contents of 10 similar containers of a commercial soap are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, an ...
Georgia Tech, CEE 3770
Excerpt: ... the mining operation. If you want 95% condence interval estimate of width 2 milligrams, how many specimens you need to sample? Assume prior knowledge indicates that pollution readings in water samples taken during a day are approximately normally distributed with a standard deviation equal to 5 milligrams. 3. The average speed of vehicles on a highway is being studied. (a) Suppose that observations on 50 vehicles yielded a sample mean of 65 mph. Assume that the standard deviation of vehicle speed is known to be 6 mph. Determine two-sided 99% condence intervals of the mean speed. (b) In part (a), how many additional vehicles speed should be observed such that the mean speed can be estimated to within 1 mph with 99% condence? (c) Suppose that Jake and Alan are assigned to collect data on the speed of vehicles on this highway. After each person has separately observed 10 vehicles, what is the probability that Jakes sample mean will exceed Alans sample mean by 2 mph? The standard deviation of ...