Exercise 3 (Modeling with random variables) An earthquake of magnitude 7 or higher occurs in the Greater California region on average every 13 years. Use the Poisson distribution to model this situation and using this model determine the probability that there will be at least one earthquake of magnitude 7 or higher next year (in the next 10 years, in the next 20 years, in the next 30 years). Reect on whether the Poisson distribution is well suited to model this situation. Exercise 4 (Modeling with random variables) We consider an urn with :r' red and 1) black balls. The balls are numbered from 1 to r + l), where the numbers 1 until 1' denote the red balls and the numbers 1" +1 until :r'+ 1) denote the black balls, respectively. We draw a <_i r balls from the urn without replacement. to model this experiment we introduce for h. x5 ball in ith draw is red black. random variable x denotes number of drawn balls. derive a suitable probability space describe and dene as maps on bonus task: distribution x1 i n. explain your answer full detail. points>