Think Different

            I saw that students are unclear about #PDF [probability density function] and #CDF [cumulative density function]. I would be glad to provide a comprehensive explanation of probability density functions ( PDFs ) and cumulative distribution functions ( CDFs ), incorporating the best aspects of the previous responses and addressing any potential shortcomings: Probability Density Function ( PDF ): A PDF is a mathematical function that describes the probability distribution of a continuous random variable. It represents the likelihood of a random variable taking on a particular value within a certain range. The PDF is always non-negative and its integral over its entire range must equal 1. For a continuous random variable X, the PDF is denoted as f(x). The probability of X falling within a certain range [a, b] is given by the integral of the PDF over that range: P(a ≤ X ≤ b) = ∫[a, b] f(x) dx. Cumulative Distribution Function ( CDF ): A CDF is...

We can use Bayes' Theorem to estimate the probability of someone not having an effect (meaning they get infected after vaccination) for both Covishield and Covaxin, considering a population of 1.4 billion individuals. Assumptions: We assume equal distribution of both vaccines in the population (700 million each). We focus on individual protection probabilities, not overall disease prevalence. Calculations: Covishield: Prior Probability (P(Effect)): Assume 10% of the vaccinated population gets infected (no effect), making P(Effect) = 0.1. Likelihood (P(No Effect|Effect)): This represents the probability of someone not being infected given they received Covishield. Given its 90% effectiveness, P(No Effect|Effect) = 0.9. Marginal Probability (P(No Effect)): This needs calculation, considering both vaccinated and unvaccinated scenarios. P(No Effect) = P(No Effect|Vaccinated) * P(Vaccinated) + P(No Effect|Unvaccinated) * P(Unvaccinated) Assuming 50% effectiveness for unvaccinated indivi...