Let us consider the weather trends in tucson during the monsoon season. let’s assume that if there is rain one day, there is a 70% chance that there will also be rain the next day. alternatively, if there is no rain on a given day, there is 20% chance that there will be rain the next day. let x denote a 2 1 vector denoting the state of weather in tucson and has the form: the probability of rain the probability of no rain        x note that probabilities are values between 0 and 1, where the value 0 denotes no chance of rain and 1 notes certain rain. a) formulate a matrix-vector expression that allows you to calculate the weather state vector for tomorrow, given the weather state vector today. b) if there is no chance of rain today, calculate the probability that it will be raining 3 days from now. c) if there is no chance of rain today, calculate the probability that it will be raining in two weeks (14 days). how does this probability change if it is certain that there is rain today? describe what you observe