3. {2D points} Suppose that the weather in Ann Arbor in July can be characterized as sunny, rainy, or cloudy [with no rain}. By looking up back issues of the Ann Arbor vas, we estimate that if it is sunny on a July day, it is equally likely to be sunny or cloudy on the next day, but it won't rain. If a July day is cloudy, there is a in percent chance that it will rain on the next day, a 25 percent chance that it will be sunny, and a 25 percent chance that it will remain cloudy without rain. If it rains on a July day, it won't he sunny the next day, and there is a ll-SI} chance of continued rain. 1) Describe the problem using a system of difference equations. 2) Assume today is sunny, compute the distribution of the weather two days later {i.e., the probability of sunny, cloudy, or rainy two days later}. 3} Give the general solution for this dynamic system. 4} Find the long-rim distribution [i.e., the steady state} of weather for July dates. 4. {25 points} Consider a univariate function f[x) = 1:" lib:2 + ?. 1) Find the points at which the function crosses the x-axjs. [Keep fractions] 2} Find the critical points of Ex}. 3) Find the inection points of f[x). 4) Use the second derivatives to find the points at which x} achieves local minimum and at which x} I 1