Weather forecasing, a markov chain problem

In a particular area, there are 2 types of weather: sunny and rainy. The following is observed across a couple year period.

• The probability of weather staying sunny the following week is 80%.
• The probability of the weather changing from sunny to rainy is 20%.
• The probability of the weather staying rainy from the following week is 70%.
• The probability of weather changing from rainy to sunny over a week is 30%.

Given this information, can you create a transition matrix and calculate the steady state vector? If you need a refresher, here is a resource on Markov Chains.