I am interested in the following random walk scenario, where a walker starts at a defined position greater than 0, say A, and then makes a "decision" to walk to either walk "b steps to the right" or walk "c steps to the left." He will choose the first option with probability p, and the second option with probability (1-p). If the walker gets to position 0 he stops. I wish to calculate: - the expectation value of the walker's position after a total of n decisions. - what happens as n approaches infinite?