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

Dashboard
Notifications
Mark all as read
Q&A

Acceptable, usual to write $\ge 2$ pipes simultaneously?

+1
−1

I'm NOT asking for the solution to this exercise that's publicly accessible. Rather, pls see the green and red underlines. If I apply the author's green definition to the red underline, then $\tilde P({\color{red}{L \mid M_2}}) \equiv P(\color{red}{L \mid M_2} \quad \color{limegreen}{\mid M_1})$.

Is it natural or wont to write $\ge 2$ Conditional Probability pipes simultaneously?

Blitzstein, Introduction to Probability (2019 2 edn), Ch 2, Exercise 26, p 87.
p 12 in the publicly downloadable PDF of curbed solutions.

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

2 comment threads

Say No To Multiple Pipes (1 comment)
Accessibility (1 comment)

1 answer

+1
−0

As mentioned in the answers you referenced in earlier versions of your question, $(-\mid-)$ is not standalone notation in usual probability theory notation.[1] Instead, $P(A\mid B)$ is just an unusual notation for a binary function. A common definition of this binary function in terms of a separate unary, unconditional probabilty function also called $P$ and the one I believe Blitzstein is using is $$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$

While I don't know how clear Blitzstein makes this elsewhere, the way to read what's being written is we're defining a new unary, unconditional probability function $\tilde P$ via $\tilde P(A) = P(A \mid M_1)$. The binary conditional probability function $\tilde P(A \mid B)$ is still defined as usual, i.e. $$\tilde P(A \mid B) = \frac{\tilde P(A \cap B)}{\tilde P(B)}$$ NOT as the meaningless $P((A \mid B) \mid M_1)$. If we want to expand $\tilde P(A \mid B)$ in terms of $P$, we get $$\tilde P(A \mid B) = \frac{P(A \cap B \mid M_1)}{P(B \mid M_1)} = \frac{P(A \cap B \cap M_1)}{P(B \cap M_1)}$$ which doesn't present any issues. The answer to (c) follows readily.


  1. I have seen it used, e.g. in Jaynes' "Probability Theory: The Logic of Science", as standalone notation, but not in a way such that $P(A\mid B)$ meant $P((A\mid B))$ where $P$ was some unconditional probability measure. ↩︎

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

0 comment threads

Sign up to answer this question »

This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!

Like what we're doing? Support us! Donate