Math Is Fun Forum

Ah I see, that's an interesting conjecture.

satwnz you can try publishing it.

Hi,

The reason why I deduce only half of Prob(X=50) is that there are 101 possible outcomes for X in a symmetry fashion.

P(X=0)=P(X=100) P(X=1)=P(X=99) ... P(X=49)=P(X=51)

P(X=0)+P(X=1)+P(X=2)+...+P(X=49) = P(X=51)+...+P(X=98)+P(X=99)+P(X=100)= 1-P(X=50)

So 1/2=P(X<50)+P(X=50)/2

Try the book

Encyclopedia of Trigonometry

by Andrew Barnes

How about Negative Binomial?

Define random variable X as the number of wins during the 100 trials. X=0,1,2,3,...,100

Prob{(100-X)-X>15} = Prob{X<43}

= 1/2 - 1/2 Prob(X=50) - Prob(X=49) - Prob(X=48) - Prob(X=47) - Prob(X=46) - Prob(X=45) - Prob(X=44) - Prob(X=43)

Excel can count the numerical answer after you apply binomial distribution formula to every point probability.

I bought a smuggled one, thank you.

0
in most of times the cosine is smaller than 1, and in the rest of times it is 1. So the absolute value converges to 0 and so do the sequence itself.

Uh Oh

West Coast of Australia hit by 50 year severest flood

The house on Grettisgata Street, in Reykjavik, is a century old, small and white, situated just a few streets from the North Atlantic. The shifting northerly winds can suddenly bring ice and snow to the city, even in springtime, and when they do a certain kind of silence sets in. This was the case on the morning of March 30th, when a tall Australian man named Julian Paul Assange, with gray eyes and a mop of silver-white hair, arrived to rent the place. Assange was dressed in a gray full-body snowsuit, and he had with him a small entourage. “We are journalists,” he told the owner of the house. Eyjafjallajökull had recently begun erupting, and he said, “We’re here to write about the volcano.” After the owner left, Assange quickly closed the drapes, and he made sure that they stayed closed, day and night. The house, as far as he was concerned, would now serve as a war room; people called it the Bunker. Half a dozen computers were set up in a starkly decorated, white-walled living space. Icelandic activists arrived, and they began to work, more or less at Assange’s direction, around the clock. Their focus was Project B—Assange’s code name for a thirty-eight-minute video taken from the math of an Apache military helicopter in Iraq in 2007. The video depicted American soldiers killing at least eighteen people, including two Reuters journalists; it later became the subject of widespread controversy, but at this early stage it was still a closely guarded military secret.

Assange is an international trafficker, of sorts. He and his colleagues collect documents and imagery that governments and other institutions regard as confidential and publish them on a Web site called WikiLeaks.org. Since it went online, three and a half years ago, the site has published an extensive catalogue of secret material, ranging from the Standard Operating Procedures at Camp Delta, in Guantánamo Bay, and the “Climategate” e-mails from the University of East Anglia, in England, to the contents of Sarah Palin’s private Yahoo account. The catalogue is especially remarkable because WikiLeaks is not quite an organization; it is better described as a media insurgency. It has no paid staff, no copiers, no desks, no office. Assange does not even have a home. He travels from country to country, staying with supporters, or friends of friends—as he once put it to me, “I’m living in airports these days.” He is the operation’s prime mover, and it is fair to say that WikiLeaks exists wherever he does. At the same time, hundreds of volunteers from around the world help maintain the Web site’s complicated infrastructure; many participate in small ways, and between three and five people dedicate themselves to it full time. Key members are known only by initials—M, for instance—even deep within WikiLeaks, where communications are conducted by encrypted online chat services. The secretiveness stems from the belief that a populist intelligence operation with virtually no resources, designed to publicize information that powerful institutions do not want public, will have serious adversaries.

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Iceland was a natural place to develop Project B. In the past year, Assange has collaborated with politicians and activists there to draft a free-speech law of unprecedented strength, and a number of these same people had agreed to help him work on the video in total secrecy. The video was a striking artifact—an unmediated representation of the ambiguities and cruelties of modern warfare—and he hoped that its release would touch off a worldwide debate about the conflicts in Iraq and Afghanistan. He was planning to unveil the footage before a group of reporters at the National Press Club, in Washington, on April 5th, the morning after Easter, presumably a slow news day. To accomplish this, he and the other members of the WikiLeaks community would have to analyze the raw video and edit it into a short film, build a stand-alone Web site to display it, launch a media campaign, and prepare documentation for the footage—all in less than a week’s time.

Assange also wanted to insure that, once the video was posted online, it would be impossible to remove. He told me that WikiLeaks maintains its content on more than twenty servers around the world and on hundreds of domain names. (Expenses are paid by donations, and a few independent well-wishers also run “mirror sites” in support.) Assange calls the site “an uncensorable system for untraceable mass document leaking and public analysis,” and a government or company that wanted to remove content from WikiLeaks would have to practically dismantle the Internet itself. So far, even though the site has received more than a hundred legal threats, almost no one has filed suit. Lawyers working for the British bank Northern Rock threatened court action after the site published an embarrassing memo, but they were practically reduced to begging. A Kenyan politician also vowed to sue after Assange published a confidential report alleging that President Daniel arap Moi and his allies had siphoned billions of dollars out of the country. The site’s work in Kenya earned it an award from Amnesty International.

Assange typically tells would-be litigants to go to hell. In 2008, WikiLeaks posted secret Scientology manuals, and lawyers representing the church demanded that they be removed. Assange’s response was to publish more of the Scientologists’ internal material, and to announce, “WikiLeaks will not comply with legally abusive requests from Scientology any more than WikiLeaks has complied with similar demands from Swiss banks, Russian offshore stem-cell centers, former African kleptocrats, or the Pentagon.”

In his writing online, especially on Twitter, Assange is quick to lash out at perceived enemies. By contrast, on television, where he has been appearing more frequently, he acts with uncanny sang-froid. Under the studio lights, he can seem—with his spectral white hair, pallid skin, cool eyes, and expansive forehead—like a rail-thin being who has rocketed to Earth to deliver humanity some hidden truth. This impression is magnified by his rigid demeanor and his baritone voice, which he deploys slowly, at low volume.

Read more http://www.newyorker.com/reporting/2010/06/07/100607fa_fact_khatchadourian#ixzz17ZazRFjz

In private, however, Assange is often bemused and energetic. He can concentrate intensely, in binges, but he is also the kind of person who will forget to reserve a plane ticket, or reserve a plane ticket and forget to pay for it, or pay for the ticket and forget to go to the airport. People around him seem to want to care for him; they make sure that he is where he needs to be, and that he has not left all his clothes in the dryer before moving on. At such times, he can seem innocent of the considerable influence that he has acquired.

Sitting at a small wooden table in the Bunker, Assange looked exhausted. His lanky frame was arched over two computers—one of them online, and the other disconnected from the Internet, because it was full of classified military documents. (In the tradecraft of espionage, this is known as maintaining an “air gap.”) He has a cyber-security analyst’s concern about computer vulnerability, and habitually takes precautions to frustrate eavesdroppers. A low-grade fever of paranoia runs through the WikiLeaks community. Assange says that he has chased away strangers who have tried to take his picture for surveillance purposes. In March, he published a classified military report, created by the Army Counterintelligence Center in 2008, that argued that the site was a potential threat to the Army and briefly speculated on ways to deter government employees from leaking documents to it. Assange regarded the report as a declaration of war, and posted it with the title “U.S. Intelligence Planned to Destroy WikiLeaks.” During a trip to a conference before he came to the Bunker, he thought he was being followed, and his fear began to infect others. “I went to Sweden and stayed with a girl who is a foreign editor of a newspaper there, and she became so paranoid that the C.I.A. was trying to get me she left the house and abandoned me,” he said.

Assange was sitting opposite Rop Gonggrijp, a Dutch activist, hacker, and businessman. Gonggrijp—thin and balding, with a soft voice—has known Assange well for several years. He had noticed Assange’s panicky communiqués about being watched and decided that his help was needed. “Julian can deal with incredibly little sleep, and a hell of a lot of chaos, but even he has his limits, and I could see that he was stretching himself,” Gonggrijp told me. “I decided to come out and make things sane again.” Gonggrijp became the unofficial manager and treasurer of Project B, advancing about ten thousand euros to WikiLeaks to finance it. He kept everyone on schedule, and made sure that the kitchen was stocked with food and that the Bunker was orderly.

At around three in the afternoon, an Icelandic parliamentarian named Birgitta Jonsdottir walked in. Jonsdottir, who is in her forties, with long brown hair and bangs, was wearing a short black skirt and a black T-shirt with skulls printed on it. She took a WikiLeaks T-shirt from her bag and tossed it at Assange.

“That’s for you,” she said. “You need to change.” He put the T-shirt on a chair next to him, and continued working.

Jonsdottir has been in parliament for about a year, but considers herself a poet, artist, writer, and activist. Her political views are mostly anarchist. “I was actually unemployed before I got this job,” she explained. “When we first got to parliament, the staff was so nervous: here are people who were protesting parliament, who were for revolution, and now we are inside. None of us had aspirations to be politicians. We have a checklist, and, once we’re done, we are out.”

As she unpacked her computer, she asked Assange how he was planning to delegate the work on Project B. More Icelandic activists were due to arrive; half a dozen ultimately contributed time to the video, and about as many WikiLeaks volunteers from other countries were participating. Assange suggested that someone make contact with Google to insure that YouTube would host the footage.

“To make sure it is not taken down under pressure?” she asked.

“They have a rule that mentions gratuitous violence,” Assange said. “The violence is not gratuitous in this case, but nonetheless they have taken things down. It is too important to be interfered with.”

“What can we ask M to do?” Jonsdottir asked. Assange, engrossed in what he was doing, didn’t reply.

His concerns about surveillance had not entirely receded. On March 26th, he had written a blast e-mail, titled “Something Is Rotten in the State of Iceland,” in which he described a teen-age Icelandic WikiLeaks volunteer’s story of being detained by local police for more than twenty hours. The volunteer was arrested for trying to break into the factory where his father worked—“the reasons he was trying to get in are not totally justified,” Assange told me—and said that while in custody he was interrogated about Project B. Assange claimed that the volunteer was “shown covert photos of me outside the Reykjavik restaurant Icelandic Fish & Chips,” where a WikiLeaks production meeting had taken place in a private back room.

The police were denying key parts of the volunteer’s story, and Assange was trying to learn more. He received a call, and after a few minutes hung up. “Our young friend talked to one of the cops,” he said. “I was about to get more details, but my battery died.” He smiled and looked suspiciously at his phone.

“We are all paranoid schizophrenics,” Jonsdottir said. She gestured at Assange, who was still wearing his snowsuit. “Just look at how he dresses.”

Read more http://www.newyorker.com/reporting/2010/06/07/100607fa_fact_khatchadourian#ixzz17ZbE98MF