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Earthquakes of many sizes (magnitudes) occur. The density function of magnitude is know to be fx ) where r 20. The design for a nuclear power plant near an active source of earthquakes will be based on the assumption that an earthquake of magnitude xo will occur where xo is chosen such that P [ X2 xol-p. If this magnitude (xo) occurs, the structure will be designed so that uninterrupted operation will continue. To avoid a nuclear incident, however the designer wants to design to resist collapse of the structure if some larger earthquake occurs. He wants to choose this other value x, such that, given that an earthquake larger than xo occurs, the probability that it will exceed x, is again p. Find x, in terms of xo, λ, and p (or fewer parameters, if possible). Find the conditional distribution of X given that X 2 xo. Find the conditional mean and variance of Xgiven that X2Xo-

Answer 1