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What is the most studied transform fault in the world?
The San Andreas Fault
The San Andreas Fault is one of the most intensely studied faults on the planet. It is a continental transform that separates the Pacific plate from the North American plate along its entire trace. The trace of the fault through California is shown in Figure 17.1.
What do u mean by convergence?
1 : the act of converging and especially moving toward union or uniformity the convergence of the three rivers especially : coordinated movement of the two eyes so that the image of a single point is formed on corresponding retinal areas.
Does transform create earthquakes?
This is known as a transform plate boundary. As the plates rub against each other, huge stresses can cause portions of the rock to break, resulting in earthquakes.
Where do most earthquakes occur?
The world’s greatest earthquake belt, the circum-Pacific seismic belt, is found along the rim of the Pacific Ocean, where about 81 percent of our planet’s largest earthquakes occur. It has earned the nickname “Ring of Fire”.
How is the harmonic mean used in math?
The harmonic mean is often used to calculate the average of the ratios or rates. It is the most appropriate measure for ratios and rates because it equalizes the weights of each data point.
Which is stronger convergence in probability or convergence in mean?
As we mentioned before, convergence in mean is stronger than convergence in probability. We can prove this using Markov’s inequality. P ( | X n − X | ≥ ϵ) = P ( | X n − X | r ≥ ϵ r) (since r ≥ 1) ≤ E | X n − X | r ϵ r (by Markov’s inequality). lim n → ∞ P ( | X n − X | ≥ ϵ) = 0, for all ϵ > 0.
Are there sequences that converge in probability but not in mean?
P ( | X n − X | ≥ ϵ) = P ( | X n − X | r ≥ ϵ r) (since r ≥ 1) ≤ E | X n − X | r ϵ r (by Markov’s inequality). lim n → ∞ P ( | X n − X | ≥ ϵ) = 0, for all ϵ > 0. The converse of Theorem 7.4 is not true in general. That is, there are sequences that converge in probability but not in mean.
When do random variables converge in the mean?
A sequence of random variables X 1, X 2, X 3, ⋯ converges in the r th mean or in the L r norm to a random variable X, shown by X n → L r X, if lim n → ∞ E ( | X n − X | r) = 0. If r = 2, it is called the mean-square convergence, and it is shown by X n → m. s. X . Let X n ∼ U n i f o r m ( 0, 1 n). Show that X n → L r 0, for any r ≥ 1.