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The relation between and are given by the following table, where the values for DRMS and 2DRMS (twice the distance root mean square) are specific to the Rayleigh distribution and are found numerically, while the CEP, R95 (95% radius) and R99.7 (99.7% radius) values are defined based on the 68–95–99.7 rule
Consider a circle in with center at the origin and radius . Gauss's circle problem asks how many points there are inside this circle of the form ( m , n ) {\displaystyle (m,n)} where m {\displaystyle m} and n {\displaystyle n} are both integers.
The resulting radius will be 1 if all angles are equal. If the angles are uniformly distributed on the circle, then the resulting radius will be 0, and there is no circular mean. (In fact, it is impossible to define a continuous mean operation on the circle.) In other words, the radius measures the concentration of the angles.
Earth has a radius of 6,357 km (at the poles) making = 6,357,000 m and the satellites have an altitude of 20,184 km [15] making their orbit radius = 26,541,000 m. Substituting these in the above equation, with Earth mass M = 5.974 × 10 24 , G = 6.674 × 10 −11 , and c = 2.998 × 10 8 (all in SI units), gives:
The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter. The area of a circle of radius R is . Given the area of a non-circular object A, one can calculate its area-equivalent radius by setting = or, alternatively:
Let tether length R = 160 yds. and silo radius r = R/(2 π) yds. The involute in the fourth quadrant is a nearly circular arc. One can imagine a circular segment with the same perimeter (arc length) would enclose nearly the same area; the radius and therefore the area of that segment could be readily computed.
Hoda Kotb’s daughters Haley and Hope will unbox an equal amount of presents on Christmas morning. But in Jenna Bush Hager’s family, it’s a free-for-all.
For a normal distribution the mean (the expected error) and the median coincide. The mean square error, MSE, is a different concept. I'd be surprised if anyone really uses the general bivariate normal case, but solving a formula involving a double integral isn't a major deal these days.