Let the speed of a vehicle be a Gaussian random variable with mean 60mph and sta

Question

Let the speed of a vehicle be a Gaussian random variable with mean 60mph and standard deviation 10 mph. That is, let X ~ N(60, 10^2). A police officer uses a radar to measure the speed of the vehicle. The measurement he got is a Gaussian random variable with mean being the speed of the vehicle, and the standard deviation of the measurement is 1/10 of the speed of the vehicle. That is, let Y | X ~ N(X, (X/10)^2). (a) What is the standard deviation of the radar? (b) Verify your result by writing a MATLAB program. Use N = 10^5 random trials to determine the variance.

Explanation / Answer

Given standard deviation is 10

New standard deviation is 1/10 of mean of speed of vehicle = 60/10 =6;

Standard deviation of the radar is 6 mph

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