a.) The arithmetic mean of the maximum daily precipitation observed in a meteorology station was calculated as 345 mm and its standard deviation as 118 mm. Assuming that the maximum daily precipitation at this station fits the Lognormal distribution, find the probability of seeing a daily precipitation of more than 500 mm in the region and the recurrence interval of precipitation with this value. ...... b.) The standard deviations of the maximum daily precipitation observed at two neighboring meteorological stations, which were observed for 24 and 30 years, respectively, were calculated as 126 mm and 172 mm, respectively. Test whether the variances obtained from these two meteorology stations are equal or not at 10% significance level. .... c.) 8 earthquakes with a magnitude greater than 6 were observed in a region within 30 years. Estimate the probability of an earthquake with a magnitude of more than 6 in the next 5 years, in the Poisson distribution.
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