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We would expect that the probability that Y returns a number between 0. Likewise, clearly the probability that the value falls between 0 and 1 must be 1, and indeed the probability that it falls between -1 and 2 must also be 1. In math:. This process is indeed correct and is called marginalization. The resulting distribution of X is called the marginal distribution.

This will not necessarily always be the case.

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Marginalization also works for PDFs, and again the only difference is that we need to use integration over all possible ys instead of sum, ie:. Of course, since you can have joint distributions of more than two variables, this visualization only goes so far, but remember our quote from last time:. Everyone does it. Marginalization allows us to get the distribution of variable X ignoring variable Y from the joint distribution of X and Y, but what if we want to know the distribution of X given a specific value of Y? This probability is called the conditional probability of X given Y, and is denoted like so:.

To give a specific example, suppose you want to know whether someone comes from Germany, and you know that they speak fluent German. You are given the following joint PMF showing the proportion of the world that speaks German and lives in Germany:. How do you know the probability that someone who speaks German is from Germany? Well it seems like you need to know how many people in the world speak German as well as how many people there are in Germany in total. In other words:. The way we get the denominator is of course using marginalization as described above, ie by summing the languages of everybody who lives in Germany.

As you might guess, the general rule is as follows:. Applying this rule to all possible values of X gives us a new distribution called the conditional distribution of X given Y. It is important to not confuse a conditional probability with something that is actually actionable. In our Germany example, it is clear that teaching someone German will not make them any more likely to be from Germany, but often this pitfall is not so obvious.

We now know how to go from a joint distribution to an marginal distribution and from a joint and marginal distribution to a conditional distribution. The process is very simple, again.

Discover how to apply deep learning models to financial data in a disciplined and interpretable way

Suppose you know the probability that someone is German given that they speak German and also the probability that someone anywhere in the world speaks German and you want to know the probability that someone is both German and speaks German. It seems like you need to simply multiply the conditional and marginal probability:. Indeed, this follow directly from the definitior of conditional probability above. Suppose we know the probability from above that someone who speaks German is from Germany as well as the probability that someone anywhere in the world is German and the probability that someone in the world speaks German.

Can we figure it out? Of course, we just need to recover the joint probability, which we did above, and then divide by the proportion of people who are from Germany. It is very useful in any number of situations, though as you can see, in spite of its fancy name, it is just a straightforward application of our definitions.

The above covers only about half of chapter 3. Captain Hammerhead and his crew complicate matters. Proteus, leader of the Guardians, kidnaps Ant so he can make the Ephemychron whole. Devil Daniels has discovered a new creature, a whale with a beautiful voice, but believes that it's a vicious and dangerous Siren.

Dolos investigates the Sargasso Sea for a lost treasure when his ship sinks because of a fish. When the Nektons tries to save him, they to become trapped in the endless sea of Seaweed and start to believe in the Curse of "The Bad Luck Fish". But soon find themselves facing off against a Male and a Female of the most ferocious and largest oceanic predators on the planet, the mighty ' Megaladon ' Shark.

Can Kaiko and Ant save Will and Fontaine from these monster sharks before they become food, or have the Nektons finally met their match? Thanks to a Giant Angler Fish , Every fish in Taiwanese waters, including Kaiko and Will fall under its spell of Bio-Luminescence, leaving Ant and Fontaine with the difficult task of sending the massive hypnotist back home without falling under its spell too.

Can Fontaine find the strength to save her family or will the challenges of the Midnight Zone cause her to crack under the pressure? Devil Daniels reveals the location of an ancient Viking shipwreck in Loki's Castle. The Nektons race to get there before Captain Hammerhead and his crew.

The Nektons find the final piece of the Ephemychron in a cave on a floating island. First Appearance: Sea Turtle Monumential.


  • The War of the Worlds.
  • Rambling On.
  • Jingles the Cat and Charlie meet New Friends: The Honey Jar Adventure (A Jingles Tale Book 3).
  • The Killer Species Series.

Ant and Fontaine meet Alpheus Benthos who says Ant is destined to be his nemesis, he lives on a sub he built with an artificial intelligence. Alpheus and Proteus are working together to find Lemuria, and Ant figures out how to use the Ephemecron.

The War of the Worlds: Book 2, Chapter 6, The Work of Fifteen Days

Nerius reveals what the terror is and that he has met Alpheus. The Nektons investigate the Baltic Sea anomaly , after finding that a symbol in the Ephemecron's map is situated at that spot. The anomaly proves to be an ancient meteor that has been tunneled by a colony of Mantis shrimp.

The Nektons investigate another spot marked on the Ephemecron's map, this one located in the Bermuda Triangle. Following the Ephemecron map, The Nektons discover a mysterious underwater maze. Trapped, separated and running out of air will they find a way out, or will the monster find them first? The Nektons discover the Dark Orca seemingly abandoned.

The ship systems are malfunctioning and strange noises make the place seem haunted, but ghosts don't show up on radar First Appearance: Lightning Ray Monumential. First Appearance: The Kraken. First Appearance: Pistol Shrimp Monumential.


  • Probability.
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  • Bank of America may be as profitable as J.P. Morgan in two years, analyst says.
  • Deep Learning and Momentum Investing!
  • Paradise Lost: Book 2.
  • Treasure Valley;
  • Computational Imaging in Orthopaedic Radiography.

First Appearance: Jellyfish Monumential. The key to her survival, she realizes, lies in deciphering her past—a past she never wanted to face again. Just the quick publication of Book Two, Arrival. From 1 worldwide bestselling fantasy author Morgan Rice comes a long-anticipated science fiction series.

Return to 20,000 Leagues Under the Sea (Luke Challenger Book 2)

SETI has received a signal from an alien civilization. Is there time to save the world? But is there time? What must he do? Fans of Young Adult Fiction will devour this latest work by Rice and beg for more. If you are, Gary John Bishop has the answer. And they bring that same fire to their narration in the audiobook. Listen to these insanely competent SEAL officers tell you exactly how to make a team successful through their firsthand experiences in business and combat.

An updated edition of the blockbuster bestselling leadership audiobook that took America and the world by storm, two U. Navy SEAL officers who led the most highly decorated special operations unit of the Iraq War demonstrate how to apply powerful leadership principles from the battlefield to business and life. Combat, the most intense and dynamic environment imaginable, teaches the toughest leadership lessons, with absolutely everything at stake.

Jocko Willink and Leif Babin learned this reality first-hand on the most violent and dangerous battlefield in Iraq. Willink and Babin returned home from deployment and instituted SEAL leadership training to pass on their harsh lessons learned in combat to help forge the next generation of SEAL leaders. After leaving the SEAL Teams, they launched a company, Echelon Front, to teach those same leadership principles to leaders in businesses, companies, and organizations across the civilian sector.

Since that time, they have trained countless leaders and worked with hundreds of companies in virtually every industry across the U.


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    4. Required listening for many of the most successful organizations, it has become an integral part of the official leadership training programs for scores of business teams, military units, and first responders. Detailing the mindset and principles that enable SEAL units to accomplish the most difficult combat missions, Extreme Ownership demonstrates how to apply them to any team or organization, in any leadership environment.

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    A compelling narrative with powerful instruction and direct application, Extreme Ownership challenges leaders everywhere to fulfill their ultimate purpose: lead and win. A former international hostage negotiator for the FBI offers a new, field-tested approach to high-stakes negotiations—whether in the boardroom or at home. After a stint policing the rough streets of Kansas City, Missouri, Chris Voss joined the FBI, where his career as a hostage negotiator brought him face-to-face with a range of criminals, including bank robbers and terrorists.

    In this practical guide, he shares the nine effective principles—counterintuitive tactics and strategies—you too can use to become more persuasive in both your professional and personal life. Life is a series of negotiations you should be prepared for: buying a car, negotiating a salary, buying a home, renegotiating rent, deliberating with your partner.

    Between busy schedules and long days, expressing love can fall by the wayside. We forget to compliment, to give gifts "just because," to linger in an embrace.