- #1

RoshanBBQ

- 280

- 0

## Homework Statement

Find [tex]\lambda= \{\lambda_i\}[/tex] with [tex]\lambda_0 = 1[/tex] if [tex]P(X_n=i+1|X_n=i) = p, P(X_n = i-1|X_n = i) = 1 - p, i \in Z, 0<p<1[/tex]

## Homework Equations

[tex]\lambda P = \lambda[/tex]

## The Attempt at a Solution

I used my relevant equation to write out:

[tex] (1-p)\lambda_0 + P\lambda_{-2} = \lambda_{-1}[/tex]

and there are infinitely more such equations, just add or subtract

*k*from all three indices into lambda. The problem is every time you add an equation, you add an unknown. I'm a bit stuck here!