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Markov models TP:

1. Draw the transition digraph corresponding to the stochastic matrix

A = ( 0,6 0,4)
(0,5 0,5)

Label the edges with the transition probabilities.

2. From your lecture: slide 12, compute the probability X= {sunny,cloudy, snowing, rainy}.

3. A particle moves on a circle through points which have been marked 0, 1, 2, 3, 4 (in a clockwise order). At each step, it has a probability (p) of moving to the right and (1 − p) to the left. Let Xn denote its` location on the circle after the nth step. The process {Xn, where n equals or more than 0} is a Markov chain. a) Find the transition probability matrix. b) Is this markov chain irreducible?

4. Each morning an individual leaves his house and goes for a run. He is equally likely to leave either from his front or back door. Upon leaving the house, he chooses a pair of running shoes (or goes running barefoot if there are no shoes at the door from which he departed). On his return he is equally likely to enter and leave his running shoes, either by the front or back door. If he owns a total of k pairs of running shoes, what proportion of the time does he run barefooted? Write transition probabilities matrix for this task.

5. Having a transition matrix:

A B C D

A 1 0 0 0

B .9 0 .1 0

C 0 .9 0 .1

D 0 0 0 1

a) Give a diagraph of the Markov chain. Vertices are states, edges should be labeled with transition probabilities.

b) If we start in state B, what is the probability of being in state A after 8 transitions? (If you can’t do the matrix multiplications, at least write out the matrix expression indicating the answer.)

c) If we start in state B, what is the probability of being in state D after 4 transitions?

d) If we start in state C, what is the probability of being in state A after 16 transitions? What is the probability of being in state D?

Hi,

I need a nice looking, simple weather application designed for the Iphone.

- Main screen: User enters a place and a time
- Next, two graphs are shown.

Probability vs. Temperature
Probability vs. Precipitation (Amount of Rain) vs. Probability

- The data for these two graphs is available from a PHP script we already have that creates XML. So, you’ll just need to pass the data the user enters into our URL, receive the XML, and then display it as graphs.

- Graphs should use colors (brigher colors for hotter temperature, cooler colors for lower temperature; dark blue colors for more precipitation and lighter colors for less precipitation)

- Should be option to show temperatures in C or F

- Should be option to show rain fall in cm or in

- Example: Main screen, user enters “Paris” and “Tomorrow”. Two graphs are shown.

Temperature graph might look like:
5%,15C
10%,16C
20%,17C
25%,18C
20%,19C
15%,20C
5%,21C,
etc.

Rainfall graph will look like:
50%,0in
25%,1in
20%,2in
5%,3in

- Navigation should be with a Tab bar at the bottom (to switch between main screen and graph modes)

Should be pretty straightforward but please ask me if you have any questions.

Also, please state whether you are also able to provide a BLACKBERRY version of the app (or only Iphone).

Please bid only for the Iphone version.

But we’d love to work with someone who we can also use again in the future to make a Blackberry version.

Thanks!