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With M = 365 days in a year, the average number of people required to find a pair with the same birthday is n = 1 + Q(M) ≈ 24.61659, somewhat more than 23, the number required for a 50% chance. In the best case, two people will suffice; at worst, the maximum possible number of M + 1 = 366 people is needed; but on average, only 25 people are ...
A little algebra shows that the distance between P and M (which is the same as the orthogonal distance between P and the line L) (¯) is equal to the standard deviation of the vector (x 1, x 2, x 3), multiplied by the square root of the number of dimensions of the vector (3 in this case).
In the case of NID (normally and independently distributed) data, the radicand is unity and θ is just the c 4 function given in the first section above. As with c 4, θ approaches unity as the sample size increases (as does γ 1). It can be demonstrated via simulation modeling that ignoring θ (that is, taking it to be unity) and using
The theoretical return period between occurrences is the inverse of the average frequency of occurrence. For example, a 10-year flood has a 1/10 = 0.1 or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year.
Once again, the answer can be reached without using the formula by applying the conditions to a hypothetical number of cases. For example, if the factory produces 1,000 items, 200 will be produced by A, 300 by B, and 500 by C. Machine A will produce 5% × 200 = 10 defective items, B 3% × 300 = 9, and C 1% × 500 = 5, for a total of 24.
If the mass of an object is estimated as 3.78 ± 0.07 kg, so the actual mass is probably somewhere in the range 3.71 to 3.85 kg, and it is desired to report it with a single number, then 3.8 kg is the best number to report since its implied uncertainty ± 0.05 kg gives a mass range of 3.75 to 3.85 kg, which is close to the measurement range.
[3] [4] The Gini coefficient was proposed by Corrado Gini as a measure of inequality of income or wealth . [ 5 ] For OECD countries in the late 20th century, considering the effect of taxes and transfer payments , the income Gini coefficient ranged between 0.24 and 0.49, with Slovakia being the lowest and Mexico the highest. [ 6 ]
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
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