FRM PART I | QUANTITATIVE ANALYSIS | COMMON UNIVARIATE RANDOM VARIABLES | CLASS 1

In this class, Sanjay Saraf Sir explains the popular distributions every FRM candidate must know: Bernoulli, Binomial, Poisson and the Exponential distribution. He also shows why the IID assumption can quietly break a risk model, and how continuous compounding connects to Poisson and default probabilities. Timestamps 0:00 - Recap of random variables and why we need common distributions 2:18 - Why the normal distribution is not enough (stock price example) 6:27 - How to revise smartly: audio summary, notes, questions and mock tests 11:30 - Full list of discrete and continuous distributions 16:32 - Bernoulli distribution: mean, variance and skew 24:12 - Binomial distribution and the IID assumption 26:45 - Why IID fails in real finance: CDO tranches and diversification 33:40 - Binomial mean, variance and the Law of Large Numbers 52:21 - Poisson distribution and how it links to Binomial 1:04:50 - Student doubt: how do you find lambda? 1:06:57 - Time value of money and continuous compounding (e^0.03) 1:12:32 - Hazard rate and survival probability of a bond 1:19:05 - Exponential distribution: time to default 1:22:49 - Class notes: Poisson 1:27:59 - Student doubt: does the number of bonds matter? 1:32:56 - Mean, variance and skew of Poisson 1:36:43 - When does Binomial become Normal? (np and nq greater than 10) 1:41:13 - When does Poisson become Normal? Claude demo setup 1:44:01 - Worked example: survival, cumulative default and default in the third year 1:53:38 - Black swans, earthquakes and deep out-of-the-money puts 1:57:46 - Claude output: Poisson vs Normal at lambda 1, 10, 100 and 1000 What you will learn: How Bernoulli, Binomial and Poisson connect to each other Why an expected value can be a number that is not even possible How e^-lambda becomes the survival probability of a bond How to calculate default probabilities across years When Binomial and Poisson start behaving like a Normal distribution Want to keep going with your FRM preparation? You can join the batch and continue your FRM journey with us. Get live classes, notes, audio summaries, question practice and mock tests, all taught in the same clear, application-first style. Join the batch: For any queries or doubts, call or WhatsApp us at Or, click this link to chat with us: Like the video, subscribe to the channel and share it with a friend who is preparing for FRM. Catalyzing Careers, Transforming Lives Sanjay Saraf Educational Institute (SSEI) is a leading coaching institute specializing in finance education. Learn. Grow. Succeed. 📞 Call/WhatsApp: