Looking for a hint on a stats proof

In summary, the conversation discusses a proof involving sets and infinite sequences of events. The goal is to prove that the probability of the union of these events is equal to the sum of the probabilities of a related sequence of sets. The conversation includes a notation explanation and a proposed approach to the proof, with the suggestion to start by showing the equality for k=1 and then proving it for k+1 assuming it holds for k.
  • #1
bennyska
112
0
so I'm somewhat new to statistics proofs, but this one is for the most part a sets proof, which i can do. I'm having trouble connecting them.
(c = complement)(AB = A intersect B)

Let A_1, A_2... be any infinite sequence of events, and let B_1, B_2... be another infinite sequence defined as B_1=A_1, B_2=A_1cA_2, B_3=A_1cA_2cA_3 and so on.
Prove that Pr(Union i=1 to n A_i) = Sum i=1 to n Pr(B_i).
(sorry if that notation is hard to understand)

So I've convinced myself that this is true. I see if i take the union of A_i up to n, that B_i up to n is equal. Each B_i is A_i minus any previous As that intersect it. I'm just having trouble saying that in math. If I had to write a proof right now, I'd say each Sum B_i = Union A_i, so they're equal.

So yeah, if i could get some hints on where to start. Thanks.
 
Physics news on Phys.org
  • #2
What does "Sum B_i" mean? Can you add sets?

I would have defined Z_k = union of A_i up to k.

Show the equality holds for k=1, and it also holds for k+1 assuming it does for k.
 
Last edited:
  • #3
i have since restarted this thread over in the homework section. i do have a proof there, if you wouldn't mind taking a peek at it, see if it looks okay. the thread has the same name as this one.
 

1. What is a "stats proof" and why is it important?

A stats proof is the process of using statistical methods to analyze and interpret data in order to make conclusions or predictions. It is important because it allows us to make informed decisions and draw accurate conclusions based on empirical evidence.

2. How do I know if I am on the right track with my stats proof?

One way to know if you are on the right track is to check your calculations and make sure they are accurate. You can also consult with a statistician or fellow researcher for feedback and guidance.

3. What are some common mistakes to avoid when working on a stats proof?

Some common mistakes to avoid include using incorrect formulas or assumptions, not properly labeling or organizing data, and not checking for outliers or other anomalies in the data.

4. How do I effectively communicate my stats proof to others?

Effective communication of a stats proof involves clearly explaining the methods used, presenting the data in a visual and organized manner, and accurately interpreting and discussing the results and implications.

5. What resources are available to help with understanding and completing a stats proof?

There are many resources available, such as textbooks, online tutorials, and statistical software programs. You can also seek guidance from a statistician or attend workshops or seminars on statistical analysis.

Similar threads

I Is an algorithm for a proof required to halt?
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Prove that every subset ##B## of ##A=\{1,...,n\}## is finite
    • Calculus and Beyond Homework Help
Replies
4
Views
500
A Proof of the inequality of a reduced basis
    • Linear and Abstract Algebra
Replies
7
Views
812
I Error(?) in proof that the rational numbers are denumerable
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
936
I Duistermaat & Kolk .... Vol II .... Proof of Proposition 6.1.2
    • Topology and Analysis
Replies
22
Views
2K
MHB Principal Ideal Domains and Unique Factorization Domains .... Bland - AA - Theorem 7.2.20 .... ....
    • Linear and Abstract Algebra
Replies
3
Views
1K
MHB Duistermaat & Kolk .... Vol II .... Proposition 6.1.2
    • Topology and Analysis
Replies
1
Views
979
I Sequences for infinitely nested radicals
    • Calculus
Replies
3
Views
2K
I Two basic results from measure theory -- on volumes of rectangles
    • Topology and Analysis
Replies
2
Views
137
A little help with a beginning stats proof
    • Calculus and Beyond Homework Help
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top