California is hit by approximately 500 earthquakes that are large enough to be felt every year. However, those of destructive magnitude occur on the average once every year (suppose earthquakes follow a exponential distribution). a) Find the probability that California will experience at least one earthquake of this magnitude during a 3-month period.

Which one is the correct answer, and why?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

Me i need ! find the asymptote and determine the end behavior of the function from the graph. the asymptote of the function is= blank 1 . for very high x-values,y =blank 2 options for blank 1 x=2 x=-2 x=3 x=-3 blank 2 options moves towards negative infinity moves toward the horizontal asymptote moves toward the vertical asymptote moves toward positive infinity