The noise voltage in a radar detection system is a Gaussian (0,1) random variable
Added by Laurie W.
Step 1
Since it is a Gaussian (0,1) random variable, it has a mean (μ) of 0 and a standard deviation (σ) of 1. This means that the noise voltage can take on any real value, but most values will cluster around the mean of 0. Show more…
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Shu N.
The noise voltage in a radar detection system is a Gaussian (0, 1) random variable N. When a target is present, the received signal is X = 6 + N volts, a Gaussian (6, 1) random variable. Otherwise, the received signal is X = N volts. Periodically, the detector performs a binary hypothesis test with null hypothesis H0: no target is present, and alternative hypothesis H1: a target is present. The acceptance sets for the test are A0 = {X <= x0} and A1 = {X > x0}. The probability of a target is P[H1] = 0.03. In the case of a false alarm, the system issues an unnecessary alert at the cost of C10 = 1 unit. The cost of a miss is C01 = 13000 units because the missed target could cause significant damage. For the MAP hypothesis test, answer the following questions. Important: if you're not using the z-table provided for this course, your answers may be marked incorrect. (a) Find the decision threshold. x0 = xMAP = (Round to 2 decimal places.) (b) Find the probability of a false alarm. PFA = (Round to 4 decimal places if the associated z-value has magnitude |z| < 2, and round to 5 decimal places when |z| >= 2.)
Sri K.
3.24 Suppose we measure the noise in a resistor (with no applied voltage) and find that the noise voltage exceeds 10 pV 5% of the time. We have reason to believe the noise is well modeled as a Gaussian random variable, and furthermore we expect the noise to be positive and negative equally often so we take the parameter, m in the Gaussian PDF to be 0. Find the value of the parameter σ². What units should be associated with σ² in this case?
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