EXERCISE 8- Find a sequence of random variables which converge almost.docx
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A sequence of random variables can converge almost surely but not in L1. For example, consider the random variables Xn that take the value n with probability 1/n and 0 with probability 1 - 1/n. Then Xn converges almost surely to 0 but does not converge in L1 since E[|Xn - 0|] = 1 does not converge to 0.
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Fault Photo 3 This photo shows two major faults - ignore the third fault at lower left. The upper fault is almost horizontal, but slightly higher on the left: it is a very low-angle, virtually sub-horizontal fault. The other fault runs from lower right just behind the white pants guy to the upper left, dipping about 40 degrees to our right. 37. For the upper fault, which is the hanging wall and which the footwall (above or below the fault)? Mark with HW and FW. 38. For the upper fault, what is the direction of motion of hanging wall relative to footwall? Given the slight incline of the fault, up to the left, is the hanging wall moving up or down? Draw half arrows to indicate relative sense of motion. 39. What kind of a fault is the upper fault? 40. For the lower fault dipping down to the right, which is the hanging wall and which the footwall? Mark these as usual with HW and FW. 41. For the lower fault, what is the direction of motion of hanging wall relative to footwall? Draw half arrows to indicate relative sense of motion. 42. What kind of fault is the lower fault? Of the mountain building faults we have discussed, one kind of fault results from regional compression, the other kind from regional extension. Both kinds of faulting in the same outcrop indicates that both opposite regional stress regimes, compression and extension, must have affected this outcrop, presumably not at the same time. If we could determine which of these faults came first, which of these faults came second and maybe cut and offset the earlier fault, we would have an idea of the sequence of events producing this outcrop. 43. Do you see any evidence of one of these faults cutting or offsetting the other? If so, please describe this and use this evidence to place the two different regional stress regimes in their correct historical order.
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Tobacco use among youth and young adults remains a serious public health problem. According to the CDC, cigarette smoking among high school students declined from 36.4% in 1997 to 8.8% in 2021. However, the use of e-cigarettes among youth has risen dramatically in recent years, increasing from 1.5% in 2011 to 27.5% in 2021. The FDA has taken action to regulate e-cigarettes and other tobacco products in an effort to help reduce youth access and appeal.
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