Number of "independent" subcubes of a hypercube
Hello, I am trying to solve this problem: I have an n-dimensional hypercube and m of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that:
- each subcube from the set may contain only those m...
Hello,
let's have this scenario. We have a parameter n and a exponentially large (in n) universe of organisms. We are given a subset of this universe, which is only polynomially large. The only action which the organisms are able to do is that two compatible organisms join together and a new...
Hello,
I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?"
Anyway, during solving this problem I came to this point:
Is the following sum exponential in 2n...
Hello,
I'm little confused about canonical and prime DNF. I found on web that prime DNF is DNF consisting of exactly the set of the prime implicants.
In school we've been told that canonical DNF is set of all prime implicants, so it gives me that prime DNF = canonical DNF.
Then we...
Homework Statement
Consider model of linear regression:
Y_i = \beta_0 + x_i \beta_1 + \epsilon_i
i = 1, ..., 5, where \epsilon_i \sim \mathcal{N}(0, \sigma^2) are independent. Find expected value and variance of predicted values \widehat{Y}_i considering that observations are...
Let's say we know this:
\sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right)
How do we get from this information to this expression of confidence interval for \theta?
\left( \widehat{\theta} \pm...
Homework Statement
Let's have random value X defined by its density function:
f(x; \beta) = \beta^2x \mbox{e}^{-\beta x}
where \beta > 0 for x > 0 and f(x) = 0 otherwise.
Expected value of X is EX = \frac{2}{\beta} and variance is \mbox{var } X = \frac{2}{\beta^2}.
Next...
Hi all,
could someone please explain to me, why, having recursively enumerable predicate Q(x,y) which is not recursive, the function defined as
f(x) \simeq \mu_{y} Q(x,y)
doesn't define partially recursive function?
Ok, here's the argument for it: the program will "try" if Q(x,y)...
Hi all,
I'm learning some calculus theory and I found one point I don't fully understand:
\mbox{Let M} \subset \mathbb{R} \mbox{ be non-empty set and let } f, f_{n}, n \in \mathbb{N} \mbox{ be functions defined on M. Then the following is true:}
f_n \rightrightarrows f \mbox{ on...
Hi all, I'm trying to compute the axis forces in the construction I put to attachment. I already have computed the R forces, but I don't know where should I start computing the axis forces from, from which point.
Could please someone give me some advice?
Thank you very much,
best regards.
Homework Statement
The bank is opened from 9:00 to 17:00. From 9:00 to 10:30 the average client count who come into bank is 32/hour, from 10:30 to 15:30 it is 26/hour and from 15:30 to 17:00 it is 50 clients per hour.
I have to test the hypothesis that the average count of clients who...
I've encountered this nice-looking inequality:
\left(A+B\right)^{p} \le p\left(A^{p}+B^{p}\right)
(p can irrational as well)
but I can't find a way to prove or disprove its correctness. I've tried using the binomial theorem, but it didn't seem it would lead me to the finish...
Homework Statement
There is k carps in the pool, m of them are marked. I randomly fish out n carps and see that x of them are marked.
What is the expected value of number of carps in the pool? (ie. expected value of number of the carps in the pool in the beginning)
How will the...
Homework Statement
Let's have 2n persons, n men and n women. Suppose they sit randomly around a table with 2n chairs. What is the probability that no two persons of the same sex will sit next to each other?
The Attempt at a Solution
Here's my idea:
I will model this situation with...
Homework Statement
Bowman shoots into a dartboard, with possible gain ranging from 0 to 10 points.
Probability that he shoots 30 points in 3 shots is 0.008.
Probability that he shoots < 8 in one shot is 0.4.
Probability that he shoots exactly 8 in one shot is 0.15.
What is the...
Hi,
I have this problem
Homework Statement
In telephone network, an average number of failures during a month for one telephone owner is 8. What is the probability that some telephone owner will experience more than 4 failures?
The Attempt at a Solution
I have no idea what...
Hi,
I can't see why these lattices aren't isomorphic:
[tex]
(\mathbb{N} \mbox{ u } \left\{-\infty, +\infty\right\}, \le) \mbox{ and } (\mathbb{N} \mbox{ u } \left\{-\infty, +\infty\right\}, \le)^{inverse}
[/itex]
I thought that this isomorphism would straightforwardly map an element...
Hi all,
I wonder if there is an isomorphism between the group of \mathbb{N} and the group of \mathbb{Q} (or \mathbb{Q}+). I know there is a proof that there is a bijection between these sets, but I didn't find a way how to construct the isomorphism.
What confuses me a little is that (I...
Homework Statement
How do the atoms and coatoms of the lattice of all subgroups of the group \mathbb{Z}(+,-,0) look like?
Homework Equations
Let (L,\le) be a lattice and e, f \in L is the minimum (maximum) elements of L. Then we say that a, b \in L is the atom (coatom) of L if a covers...
Hi all, I just wrote a test from probability and had troubles doing this problem:
Homework Statement
The assurance company makes an insurance for 1000 people of the same age. The probability of death during the year is 0.01 for each of them. Each insured person pays 1.200 dollars a year. In...
Homework Statement
Meteorologists expect rapid temperature drop in the following 48 hours. What is the probability that the temperature drop will occur between 15:45 and 24:00?
The Attempt at a Solution
I can't find out, what distribution is suitable for this kind of problem...Would...
Hi all!
I have a problem solving this exercise:
Homework Statement
Peter and Paul play a card game and after each round the winner gets (and the defeated pays) one dollar. Both of them have equal chance to win in the round, the round can't end in a tie.
Homework Equations
a) Find out...
Hi all!
Homework Statement
What I'm trying to figure out is a reaction of a solid desk (don't know if this is the proper term) given this picture:
http://twoflower.matfyz.cz/inc/eng.gif [Broken]
I need to compute the reactions A, B and C (they corresponding to points denoted by 'a'...
Hi all,
I encountered a problem I don't know how to solve: In \mathbb{Z}_{21}, I want to find numbers x such that x^2 = x.
I don't know what to do with that, I just wrote that (since 21 divides x^2 - x)
21y = x^2 - x
for some integer y, but it didn't seem to help me much...
Hi all,
I've been practising some algebra excercises and don't know how to solve this one:
Given the group (\mathbb{Z}_{12}, +, 0), find all its subgroups. How many elements will have these subgroups?
The only idea which came to my mind is to see the subgroups generated by each...
Hello all,
first I hope there's no problem putting this question here, since I didn't find any special forum dedicated to propositional logic.
I really have very basic question, I'm trying to prove
\vdash (A \rightarrow (B \rightarrow C)) \rightarrow (B \rightarrow (A \rightarrow C))...
Let
G \subset \mathbb{R}^{n}\mbox{ open }
a \in G
f : G \rightarrow \mathbb{R}
f \in C^{1}(G)
Df(a) = \overrightarrow{0}
Then:
(i) if D^2f(a) is positively definite, then f has local minimum in a
(ii) if D^2f(a) is negatively definite, then f has local maximum in a
(iii) if...
Hi all,
you all sure know this theorem. We've it as follows:
Let
(P,\rho)
be metric space, let
K \subset P
be compact and let
f:\ K \rightarrow \mathbb{R}
is continuous with respect to
K.
Then
f
has its maximum and minimum on
K.
Proof:
f(K)
is compact (we know from previous...
Hi,
can somebody see if there is a way to solve this analytically?
x = \mbox{cotg } x
I know it could be solved numerically, but I'm interested in analytical solution only (if it exists, of course).
Thank you very much.