LOR16: The quantile function, the survival function and the PDF
In this episode, building on the cumulative distribution function F (CDF) introduced in Episode 15, we define the quantile function Q, the survival function S, and the probability density function f (PDF). We then explore how each of these tools helps describe the behavior of a random variable.Along the way, we also introduce Value-at-Risk (VaR), which becomes quite straightforward once you understand quantiles.Are you ready to take the risk?Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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14:01
LOR15: The cumulative distribution function of a random variable
In this episode, we continue laying the foundations of our mathematical treatment of risk. In particular, we introduce the cumulative distribution function, or CDF, as a tool for describing the probabilistic behavior of a random variable. We illustrate this with a simple example and discuss the basic characteristics of this interesting non-decreasing function, which will soon help us address very practical matters.Are you ready to take the risk and follow Galileo's suggestion?Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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14:12
LOR14: Sigma-algebras and probability spaces
In this episode, we answer the question we left hanging at the end of Episode 13: What is a sigma-algebra?We will explore the properties of a sigma-algebra and explain why we want our event space to be one. Next, we will discuss probability spaces in a simple yet rigorous way, which will set the stage for understanding random variables and the mathematical treatment of risk measures.Finally, we will discover why it can be inconvenient to swim naked.Are you ready to wear a swimsuit?Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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16:40
LOR13: Back to risk, introducing risk measures
In this episode, we come back to the definition of risk and start discussing how we can measure it. That is why we need to introduce risk measures. But that requires us to be more formal and speak about the sample space and the event space in a more mathematical way.Ready to discover the power set?We are paving the way to introduce the probability space, a pivotal concept for us.Ready to take the risk?Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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17:09
LOR12: Keynes, Jeffreys, Jaynes and finally Kolmogorov
In this episode, we conclude our overview of the various schools of thought on probability.We begin by examining the logicist perspectives of Keynes, Jeffreys, and Jaynes before transitioning to Kolmogorov's axiomatic definition.We will briefly review the three basic axioms of probability and explain why the axiomatic approach is not a definition in the traditional sense, but rather a framework that transcends the objectivist–subjectivist debate.Are you ready to take the risk?Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
A podcast about risk, probability, philosophy and data science.Become a supporter of this podcast: https://www.spreaker.com/podcast/the-logic-of-risk--6469023/support.
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