## probability – Assume that \$ A \$ and \$ B \$ are independent events. For a \$ C \$ event such as \$ P (C)> \$ 0, prove that \$ A \$ event donated \$ C \$

assume $$A$$ and $$B$$ are independent events. For an event $$C$$ such as $$P (C)> 0$$ , prove that the event of $$A$$ given $$C$$ is independent of the event of $$B$$ given $$C$$

We have A and B are independent so $$P (AB) = P (A) cdot P (B)$$

We must show that $$P ((A mid C) cap (B mid C)) = P (A mid C) cdot P (B mid C)$$

My procedure was like that
$$P ((A mid C) cap (B mid C)) = P ((A mid C) mid (B mid C)) cdot P (B mid C)$$
$$= frac {P (AB mid C)} {P (B mid C)}$$

I played until I got this
$$frac {P (AC)} {P (C)} cdot frac {P (B mid AC)} {P (B mid C)}$$
Now the first part gives us $$P (A mid C)$$ . I could not get from the second part the missing part that is $$P (B mid C)$$.

Is my procedure correct? If so, how can I find the second part?

## Hostwinds Client – Can I Assume that a hacking is the fault of my host?

Hi guys,

This may therefore seem like a random place to post this, but I received very informed answers the last time I thought it was worth trying.

So I discovered yesterday that my hosting account (with Hostwinds) had been hacked. I was checking one of my domains and I noticed that he was being redirected to an ecommerce website and that he was becoming suspicious. I've checked a few and the same thing.

I immediately alerted Hostwinds who had informed me that my account had been hacked and had somehow "corrected" things (they were able to remove the degrading content from my pages and then launch an anti-malware analysis).

Unfortunately, I woke up today to find that the sites have been hacked again and the situation is even worse. Basically, every WordPress site that I run (about 10, including a few that I manage for my family members) contains PHP code and a link to a website to buy jerseys. The worst thing is that my areas of activity are done and I just sent them to a group of potential customers.

Here is my question

I do not remember when I hosted my first estate, but I guess it was ten years ago. I have never been hacked until yesterday. I always keep WordPress and all plugins updated.

Is it safe to assume that this is due to the miserable servers of my host? Hostwinds did not really impress me and my first assumption (especially when they "solved" the problem then that he came back the next day) was that he did not get it wrong. acted as another manifestation of their incompetence.

TIA!

## Terminology – What Can I Assume When Examining Computer Science AP?

I plan to take the Computer Science AP exam in May and I'm trying to practice using standard questions. I used Barron's practice test and came across this question:

As a regular Java user, inheritance has not been a confusing topic for me, but the answer to this question really troubles me. While I knew that A was correct, C should also be. The point of private members is only accessible in a class. Of course, you can use accessors, but the member is not accessible in itself, which the option seems to indicate. If I can just say that accessors can be used, why should we consider the privacy of members? So, my general question is: what can I safely assume on the AP CS exam? Will questions like this come up? I know this is not the best forum to ask questions about this, but the only other way I could find is CollegeConfidential, which crashed after trying to sign up.

## lo.logic – Can we assume a contradiction in a proof?

In PA, we can note m | n for n is divisible by m. To prove (4 | n) → (2 | n), we generally assume that 4 | n then deduces 2 | n and conclude (4 | n) → (2 | n).

But we have ¬ (4 | 5), so ¬∀n (4 | n), or in other words n (¬ (4 | n)). Assume that 4 | n is in contradiction with ¬∀n (4 | n) and n (¬ (4 | n)) because the generalization of 4 | n is n (4 | n).

The question is then: could we assume something in a proof even when it could lead to a contradiction? If no, how to legitimize the evidence above?

## This girl says that I am the father of her baby, but I refuse to assume her responsibilities until proven otherwise.

I think she's stupid and you may be in the same boat as her.

It is easy to reproduce with someone, but it is difficult for many people to take charge and choose the right partner. Nowadays, choosing a partner is optional.

I think she should have an abortion and stop recurring. I can tell you right now that she will be an unfit mother and that the father is a loser.

.

## Let T be a linear operator of a vector space of dimension n V on a field F. Assume that T is nilpotent. Show that \$ T ^ n = 0 \$.

Let T be a linear operator of a vector space of dimension n V on a field F. Assume that T is nilpotent. CA watch $$T ^ n = 0$$.

I've seen people prove it by arguing with minimal polynomials. Can any one prove that without such an argument?

## Why do people assume that if someone is liberal, it means we are communists?

All forms of socialism have in common that
1.
you intend to replace capitalism with an allegedly better and more just system, based on the fact that the government uses its legal monopoly of aggression to force and threaten people to obey
2. By moving the price mechanism, you can neither
2.1 know, neither
2.2 calculate
if you use rare factors to better meet the most urgent needs and needs of people, as defined by their subjective needs *, whatever your definition of the ultimate human well-being criterion *.

This means that you are wrong, that you have been baffled by superficial appearances and labels on which you have been brainwashed – by the durr government!

You have not understood that you do not believe in capitalism to the extent of your social democracy or democratic socialism.

Your whole ideology is defined by forcibly forcing voluntary transactions and individual liberties, to force people to sacrifice their values, based on the Marxoid ideology of class warfare and the alleged exploitation of job.

So your idea that you are a form of capitalist or libertarian is completely false, and to the extent that it is correct, you are completely contradicting yourself with your ideology of the left.

In reality, you believe in unlimited government power over everything and anything, and to the extent that you do not do it, it's because you're a libertarian, NOT a social democrat or a democratic socialist .

Socialist Democrats do not even believe in democracy. Take Trump for example. If voters elect a non-socialist government, they do not just say, "That's good, because we believe in democracy and accept the legitimacy of a non-socialist government elected by democracy."

No-o-o-o. They do what they are doing: hating, resisting, throwing up, and "completely rejecting" the legitimacy of ANY NON-socialist government.

So how can you say that they are "democratic" socialists, if they do not accept that democracy does anything other than elect socialists and if they resist violently any other democratic result?

So socialist democrats are not socialist democrats: they are simply old totalitarian socialists, always.

Like you.

But if I'm wrong, then * indicate what limits the legitimacy of government power *.

You can not answer because you are a totalitarian.