[1] Consider the Sunny-Rainy example we covered in class but suppose that the tran- sition matrix is given by the following matrix instead [0.8 0.2] P = 0.5 0.5 a) Suppose that at some time t, the weather is S or R with equal probability. Write down the state vector Tt and then compute t+1 and 7t+2, i.e. compute the probabilities that the weather will be S or R in t + 1 and t + 2. b) Suppose that at some time t, the weather is twice more likely to be Sunny than Rainy. Write down the state vector Tt, and then compute 7+1 and Tt+2. c) Find the stationary distribution corresponding to the transition matrix given above using the equation that defines stationarity. d) Suppose that at some time t, the weather is Sunny with probability 5/7. Compute the state vector for time t + 1 and t + 2. Did you expect these results? Explain your answer.

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Please Solve using R calculator or excel. Show all work. Thank You.

A runner goes for a run. On the first part of the run, she runs 2 miles in 13 minutes. On the second part of the run, she runs 3 km in 20 minutes what is her average speed?(must include units)

Brock rides his bike 22 1/8 miles to the nature preserve. On his way home, after 16 1/5 miles, he stops at a deli for lunch. How far is Brock from home?