The circular probable error (CPE) is a measure of accuracy for a shooting system of a toy rifle at the target on the (x, y) plane. A boy shoots at the target on the (x, y) plane. The actual point in which the shooting hits the target on the (x, y) plane is assumed to follow a bivariate normal distribution with the means μx = μy = 0, standard deviations 0x =σy = 0 and correlation coefficient p = 0. The CPE of the boy is defined as the radius of a circle centred at (0, 0) with a probability 0.5 to encompass (X, Y), i.e., the point where the shooting hits the target. If r = CPE, then Pr(√x² + y² ≤r)=0.5. Derive a formula for r in terms of o.
The circular probable error (CPE) is a measure of accuracy for a shooting system of a toy rifle at the target on the (x, y) plane. A boy shoots at the target on the (x, y) plane. The actual point in which the shooting hits the target on the (x, y) plane is assumed to follow a bivariate normal distribution with the means μx = μy = 0, standard deviations 0x =σy = 0 and correlation coefficient p = 0. The CPE of the boy is defined as the radius of a circle centred at (0, 0) with a probability 0.5 to encompass (X, Y), i.e., the point where the shooting hits the target. If r = CPE, then Pr(√x² + y² ≤r)=0.5. Derive a formula for r in terms of o.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text:The circular probable error (CPE) is a measure of accuracy for a shooting system of a
toy rifle at the target on the (x, y) plane. A boy shoots at the target on the (x, y) plane.
The actual point in which the shooting hits the target on the (x, y) plane is assumed to
follow a bivariate normal distribution with the means μx = μy : 0, standard deviations
σχ= Gy = 0 and correlation coefficient p = 0. The CPE of the boy is defined as the
radius of a circle centred at (0, 0) with a probability 0.5 to encompass (X, Y), i.e., the
=
point where the shooting hits the target. If r = CPE, then Pr(√X² + y² ≤r)=0.5.
Derive a formula for r in terms of o.
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