This may be modelled by a markov chain with transition matrix 0.8 * 0.65| By determining the missing entries in the matrix find the likelihood that the weather is raining 2 days from now if it is currently clear.

A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of rainy and drought for known initial year.(a) Write out the stochastic matrix.(b) Find the probabilities for:(i) Year 1(ii)

Solve bout the volume of securities sold by a brokerage firm, using the following data:

why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion

Please don't copy from any other website or google, I need correct and proper explanation

We will use Markov chain to model weather XYZ city. According to the city’s meteorologist, every day in XYZ is either sunny, cloudy or rainy.  The meteorologist have informed us that the city never has two consecutive sunny days.  If it is sunny one day, then it is equally likely to be either cloudy or rainy the next day.  If it is rainy or cloudy one day, then there is one chance in two that it will be the same the next possibilities.  In the long run, what proportion of days are cloudy, sunny and rainy? Show the transition matrix.

A factory worker will quit with probability 1/2 during her first month, with probability 1/4 during her second month and with probability 1/8 after that. Whenever someone quits, their replacement will start at the beginning of the next month. Model the status of each position as a Markov chain with 3 states. Identify the states and transition matrix. Write down the system of equations determining the long-run proportions. Suppose there are 900 workers in the factory. Find the average number of the workers who have been there for more than 2 months.

If A is a Markov matrix, why doesn't I+ A+ A2 + · · · add up to (I -A)-1?

Define Markov matrix.

A square matrix is said to be doubly stochastic if itsentries are all nonnegative and the entries in each row andeach column sum to 1. For any ergodic, doubly stochasticmatrix, show that all states have the same steady-stateprobability.