Probability of coin and markov transition matrix

[hupdy]

1. Consider n flips of a fair coin. Calculate the probability:

a. n/2 < -Total number of heads

b. 5000 > total #heads

c. n/2 < total #heads < 5n/8

d. n < total #heads.

WHERE n = 8992

2. Consider the shopping problem
Markov transition matrix

.5 | .5
-----------------
.75 - k | .25 + k

where k = 8992 divided by 20000..

Start with initial v0 = (..5,.5) and describe the behavior of the
system for many time steps.

Does your result cycle, does one state become extinct, or does it
approach a limit value?Any help will be nice.

 

[cristo]

Is this a homework question? If so, please post your attempts at a solution, before we can help you.

 

[CRGreathouse]

If you calculate the answer to #1a exactly, there are 2706 digits in the numerator and the same number in the denominator.