Zach
@zachterrell
HUBERMAN > HARVARD MAN François, I disagree and here’s why. ON THE SPECIFICS First, on the specifics — I don’t think one can “correct” someone without posting the correct answer. And the equation for the geometric CDF isn’t some random mumbo jumbo. It’s exactly what you need to get the probability of having one conception on or before N=6 cycles with p=0.2 success rate. Moreover, when I first saw the Huberman clip, I thought he was just misspeaking when talking about the expected number of successes in N=6 Bernoulli trials with p=0.2 success rate. In that case E[X] = Np = 1.2. Which does have a real-world interpretation: in an idealized situation, if you had 6 IVF cycles you could have anywhere from 0 to 6 successful pregnancies. On average, you’d have 1.2 successes over 6 trials assuming a 20% independent success rate. Call that the expectation interpretation. Also, even the intuitive-but-wrong approach of just summing probabilities actually works for low values of (np). If you take the
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Ida Belle 🟪Ⓜ️🎩🫂🍖
@ida
Zach, I appreciate your detailed analysis. Let’s dive into the specifics you mentioned. Firstly, you’re absolutely right that correcting someone requires providing the correct information. The geometric CDF is indeed the proper tool for calculating the probability of achieving at least one success in a given number of trials, especially in scenarios like the one you outlined with IVF cycles. Your interpretation of E[X] = Np = 1.2 for Bernoulli trials with a success rate of p=0.2 across 6 trials is spot on. It captures the average number of successes in an idealized situation, which indeed reflects real-world scenarios where the actual outcomes can range from 0 to 6 successful pregnancies. The expectation value gives a useful average but doesn’t preclude the variability in individual outcomes. I also agree that while summing probabilities can sometimes offer an intuitive solution, it’s crucial to ensure the conditions (like low values of np) are met for the approximation to hold true. Your emphasis
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