# Math

posted by .

Let p>q>0 with p+q = 1 and a = q/p < 1.

Let X_n denote the random walk with transitions
X_{n+1} = CASE 1: X_n + 1 with probability p and CASE 2: X_n - 1 with probability q.

For i â‰¥ 0, we set u_i = P(X_n = 0 for some n â‰¥ 0|X_0 = i).

Give the value of u_0.

## Similar Questions

1. ### mathematical statistics

Suppose a_n∈ [0,1] and X_n is a sequence of i.i.d random variables with p.d.f : p(X_n=1)= p(X_n= -1)=0.5 . ∑_(n=1)^∞▒a_n X_n is convergent with probability 1, is ∑_(n=1)^∞▒a_n^2 convergent?
2. ### mathematical statistics

Suppose X_n is a sequence of independent Bernoulli random variables and p(X_n=1)=p_n. If Y=∑_(n=1)^∞▒X_n is convergent with probability 1 ,is E(Y) convergent?
3. ### Math Proof

Let {X_n} be a sequence of real numbers that is bounded above by M and such that X_n-->x Prove that x<=M
4. ### Poofs

Let {X_n} be a sequence of real numbers that is bounded above by M and such that X_n-->x Prove that x<=M. This is what I have, but I believe it is wrong: Let M>0 then there exist N>=1 s.t. n>=N. then |x_n - x|<M. …
5. ### Proof

Let {x_n} and {y_n} be real valued sequences suppose x_n->0 and {y_n} is bounded. Prove that (x_n*y_n)->0
6. ### Sequences

If {x_n} is not bounded above, does x_n -> infinity?
7. ### math

x_1=3/2, x_(n+1)=3/(4-x_n) prove that the series x_n converges and find its limit.
8. ### Math

Given an iterated map, ie. x_n+1 = 3* x_n / (x_n +1), how do we find all of its fixed points?
9. ### Math

Use Newtons Method to find 13^(1/4) correct to four decimal places. I know the formula X_(n+1)= X_n - [f(X_n)]/[f'(X_n)]. I am not sure how to go on from there. I made the equation into y=X^(1/4), but I can't seem to figure out how …
10. ### math

If lim┬(n→∞)⁡〖(x_n-x)/(x_n+x)〗=0, prove that lim┬(n→∞)⁡〖x_n 〗=x.

More Similar Questions