Understanding Recurrence in Probability: Solving for hN(1) and cNcN

In summary, the conversation discusses setting hN(1) equal to cN and solving for it. The goal is to determine if 0 is recurrent when qx/px = infinity. The individual is confused on how to solve for hN(1) and was not able to draw a conclusion based on the given equation.
  • #1
shahawn11
2
0
Homework Statement
I have to set hN(1) = cN and solve it. Afterwards I need to conclude that 0 is recurrent if and only if qx/px = infinity
Relevant Equations
Equations are in the image below
Exam 1 Problem 6.PNG


I set hN(1)hN(1) equal to cNcN, but I'm confused on how I'd be able to solve it and because of that I was not able to conclude that 0 is recurrent when qx/px = infinity
 
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  • #2
shahawn11 said:
Homework Statement:: I have to set hN(1) = cN and solve it. Afterwards I need to conclude that 0 is recurrent if and only if qx/px = infinity
Relevant Equations:: Equations are in the image below

View attachment 257753

I set hN(1)hN(1) equal to cNcN, but I'm confused on how I'd be able to solve it and because of that I was not able to conclude that 0 is recurrent when qx/px = infinity
Start by setting ##h_N(1) to ##c_N##. What do you get when you do this?
It is not enough to tell us what you tried -- you need to show us what you tried.
 

1. What is recurrence in probability?

Recurrence in probability refers to the concept of an event or outcome repeating itself over a series of trials or experiments. It is often used to analyze the long-term behavior of a system or process.

2. How is recurrence calculated in probability?

Recurrence can be calculated by finding the probability of an event occurring at least once in a given number of trials. This can be represented mathematically as hN(1), where h is the probability of the event and N is the number of trials.

3. What is the significance of hN(1) in recurrence?

hN(1) is an important measure in recurrence as it represents the probability of an event occurring at least once in a given number of trials. It can help determine the likelihood of an event happening in the long run and can be used to make predictions about future outcomes.

4. How is cNcN used in recurrence calculations?

cNcN is a measure used to determine the number of ways an event can occur in a given number of trials. It is often used in conjunction with hN(1) to determine the overall probability of recurrence in a system or process.

5. What are some real-world applications of recurrence in probability?

Recurrence in probability has many practical applications, such as predicting stock market trends, analyzing the behavior of complex systems, and understanding the spread of diseases. It is also used in statistical analysis and decision-making in various industries, including finance, healthcare, and engineering.

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