Chapter 12 , Q 12.1

Chapter 12 , Q 12.1 ???

 

Given a random walk , probability of moving to right is p and left is q = 1-p.

What is the probability that reaching the postion 10 in 10 moves. Just assume that u hv started at the origin, no moves taken yet ,,i,e u r at zero th postion..thats why it is given X0 = 0...

Assume that u take 1 position in each move in either side with the given probability..

so with 10 moves u can reach the 10th postion if u move in same direction in every move...

So think of Binomial distribution, reaching the postion 10 in 10 moves, given the prob of moving to right is p..
P(X10 = 10) = 10 c 10 * p pow 10 * (1-p) pow 0 = P pow 10.

And reaching 10th postion in 2 moves is impossible that why
P(X2 = 10) = 0.

Since the probabilities are not equal, the walk is not stationary.

Thanks & Regards,
Nagesh.