# Tagged Questions

0answers
43 views

### Event probability prediction from multiple observations

I am programming some fuzzy logic for an application I'm developing, and I'm not sure how to "combine" multiple fuzzy boolean observations into a guess. Each of my fuzzy boolean observations describes ...
3answers
180 views

### Boolean algebra probability not coming out right

Assuming A,B,C,D are mutually independent. $P[(A\cup\overline{B}\cup C)\cap(A\cup C \cup \overline{D})]$ I get $(P(A) + 1 - P(B) + P(C))(P(A) + P(C) + 1 - P(D))$ But when I plug in the numbers, I ...
1answer
67 views

### The fraction of k-juntas with low influences in all of the coordinates

Let $f:\{-1,1\}^n\to\{-1,1\}$ be a boolean function. Define the influence of the $i$'th coordinate of $f$ as follows: $$\operatorname{Inf}_i(f)=\Pr_{x}[f(x)\neq f(\hat x_i)]$$ where $x$ is uniformly ...
1answer
205 views

### A Boolean function with total influence 1 must be a dictatorship

Let $f:\{-1,1\}^n\to\{-1,1\}$ be a boolean function. Define the influence of the $i$'th coordinate of $f$ as follows: $$\operatorname{Inf}_i(f)=\Pr_{x}[f(x)\neq f(\hat x_i)]$$ where $x$ is uniformly ...
2answers
75 views

### Parity is the only function with maximal influences

Let $f:\{-1,1\}^n\to\{-1,1\}$ be a boolean function. Define the influence of the $i$'th coordinate of $f$ as follows: $$\operatorname{Inf}_i(f)=\Pr_{x}[f(x)\neq f(\hat x_i)]$$ where $x$ is uniformly ...