Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

In $w_{k + 1} - w_k = (\frac{1 - p}{p})^{exponent}(w_1 - w_0)$, why isn't exponent $k + 1$?

+1
−2

Please see the $r^k$ underlined in red, which is $(\frac{1 - p}{p})^k$ as defined by the green underlines.

  1. How do you deduce that the exponent must be $k$? Why isn't the exponent $k + 1$?

  2. Is this question related to the Fence Post Error? Have I committed it?

Image alt text

Tsitsiklis, Introduction to Probability (2008 2e), p 63.

History
Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

0 comment threads

1 answer

+1
−0

If you set $k=0$ the equation becomes $$w_{0+1} - w_0 = r^{\textrm{exponent}}(w_1-w_0)$$ For this equation to hold (in general) the exponent must be zero and not one. Thus an exponent of $k+1$ must be wrong.

I think the problem is not a fence-post problem but the proper base case for the induction. Try to write down the step of going from $$w_{k+1} - w_k = r (w_k-w_{k-1})$$ to $$w_{k+1} - w_k = r^k (w_1-w_0)$$ as a proper proof by induction.

History
Why does this post require moderator attention?
You might want to add some details to your flag.

1 comment thread

"For this equation to hold (in general) the exponent must be k = 0 and not k + 1 = 1". What do you me... (3 comments)

Sign up to answer this question »