SECTION 8.3. Bayesian Least Mean Squares Estimation Problem 10. A police radar always overestimates the speed of incoming cars by an amount that is uniformly distributed between 0 and 5 miles/hour. Assume that car speeds are uniformly distributed between 55 and 75 miles/hour. What is the LMS estimate of a car's speed based on the radar's measurement?
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We are given that $X$ is uniformly distributed between 55 and 75 miles/hour, and $Y$ is uniformly distributed between $X$ and $X+5$ miles/hour. Show more…
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A police radar always overestimates the speed of incoming cars by an amount that is uniformly distributed over the interval of 0 and 5 miles/hour, independent of the actual speed of the car. Assume that car speeds are uniformly distributed over the interval of 55 and 75 miles/hour. (a) Find the linear MMSE estimator of a car’s speed based on the radar’s measurement. Find the resulting MSE. (b) Find the MMSE estimator of a car’s speed based on the radar’s measurement. Find the resulting MSE and compare it with that of the linear MMSE estimator obtained in (a).
Aishwarya K.
Ivan K.
Part B: Probability Distributions (10 Marks) Data that has been gathered from a recently constructed toll road is summarized below: • The average rate of traffic flow was 20 cars per minute. • The speed of the cars was normally distributed with a mean of 65 km/h and a variance of 5 km²/h². • Within a 3 day period, 90% of verhicles had paid their toll, while 10% has not. Based on the information, you need to answer the following questions by hand and verify using an in-built MATLAB function (eg. binopdf). 1. In a random sample of 10 cars, what is the probability exactly 2 have not paid their toll. 2. Within a 5 second period, what is the probability of seeing less than 2 cars? 3. What is the proabability that a random car is speeding given the speed limit is 70 km/h? 4. What range of speeds are in the interquartile range? (Note: the interquartile range is the middle 50% of speeds).
Sri K.
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