This is in response to the following request:
A parent particle divides into 0,1,or 2 particles with probabilities 1/4,1/2,1/4.it disappears after splitting.let Xn denotes the number of particles in n-th generations with X0=1.find P(X2¿0) and the probabilities that X1=2 given that X2=1.
For my first entry I will try to answer the question.
Let and be the nonzero probabilities of dividing into 0, 1, or 2 particles, and let denotes the number of particles at the generation.
With , find 1) and 2)
1) After two generations there can be at most particles so
Note that if , then .
Using your values I get 3/32.
2) From the definition of conditional probability
Why? To get to , at there are either one or two particles, if there is one particle it remains one at , and if there were two particles at , then one has to go to zero and the other one—this can happen two ways.
Using your values I get 2/3.
Now I have a question for you to think about. What happens in the long run, as ?
|Date of creation||2013-03-22 19:11:21|
|Last modified on||2013-03-22 19:11:21|
|Last modified by||statsCab (25915)|