MHB Modified Random Walk: Expected Duration and Recurrence Equation Analysis

AI Thread Summary
The discussion focuses on deriving a recurrence equation for the expected duration of a modified random walk by conditioning on the first step. It presents a specific equation format involving expected values and parameters represented as ˜p, ˜q, and ˜c. Participants are asked to identify these parameters in relation to the original variables p, q, and r. Additionally, there is a request for clarification on the definition of the modified random walk. The conversation emphasizes the mathematical formulation and relationships necessary for analysis.
Poirot1
Messages
243
Reaction score
0

(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.​
Ea = ˜pEa+1 + ˜qEa1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks
 
Physics news on Phys.org
Poirot said:

(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.​
Ea = ˜pEa+1 + ˜qEa1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks


Please post the entire question, in particular the definition of your modified random walk

CB
 
Hello, I'm joining this forum to ask two questions which have nagged me for some time. They both are presumed obvious, yet don't make sense to me. Nobody will explain their positions, which is...uh...aka science. I also have a thread for the other question. But this one involves probability, known as the Monty Hall Problem. Please see any number of YouTube videos on this for an explanation, I'll leave it to them to explain it. I question the predicate of all those who answer this...
I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
Back
Top