Transition probabilities of markov chain

Assignment Help Basic Statistics

Reference no: EM131005732

Suppose the numbers of families that check into a hotel on succes- sive days are independent Poisson random variables with mean λ. Also suppose that the number of days that a family stays in the hotel is a geometric random variable with parameter p,0 p 1. (Thus, a family who spent the previous night in the hotel will, independently of how long they have already spent in the hotel, check out the next day with probability p.) Also suppose that all families act independently of each other. Under these conditions it is easy to see that if Xn denotes the number of families that are checked in the hotel at the beginning of day n then {Xn, n 0} is a Markov chain. Find

(a) the transition probabilities of this Markov chain;

(b) E[Xn|X0 = i];

Reference no: EM131005732

Questions Cloud

Calculate the entropy of propane at its critical point : Use the Lee-Kesler method- Calculate the entropy of propane at its critical point. The reference state is the ideal-gas state at the critical point.

Coin ?ipped on monday comes up heads : Suppose that the coin ?ipped on Monday comes up heads. What is the probability that the coin ?ipped on Friday of the same week also comes up heads?

Determining the transition probability matrix : Let Xn denote the state of the system after the nth step. Explain why {Xn, n = 0, 1, 2, .. .} is a Markov chain and calculate its transition probability matrix.

Calculate the entropy change of propane : Propane is isothermally compressed from 0.01 bar, -51.4 °C to 17 bar. The process takes place reversibly in a closed system. Draw the PV graph of the process.

Transition probabilities of markov chain : (a) the transition probabilities of this Markov chain; (b) E[Xn|X0 = i]; (c) the stationary probabilities of this Markov chain.

Calculate the heat that must be supplied to the system : n-Octane is compressed reversibly at constant temperature along the critical isotherm until the critical point is reached. The initial pressure is 1 bar. The pressure takes place in a closed system. Use the Lee-Kesler method to calculate what is t..

Problem regarding the production process : 1. The rate at which the production process goes from up to down (that is, the rate of breakdowns); 2. The average length of time the process remains down when it goes down; and 3. The average length of time the process remains up when it goes up.

Calculate the net amount of work that is produced : Calculate the ratio of the network over the amount of heat absorbed at the high temperature of the cycle. How does this value compare to the theoretical efficiency of the Carnot cycle that is calculated based on the two operating temperatures?

The electrophilic aromatic substitution of benzoic : Could somebody please help me write out the mechanism for the Electrophilic Aromatic Substitution of Benzoic Acid to produce m-nitrobenzoic Acid?

User Account

All Pages