Prob & Stats 20B: Maximum Likelihood Estimation for Geometric Distribution скачать в хорошем качестве

Prob & Stats 20B: Maximum Likelihood Estimation for Geometric Distribution

What does Maximum Likelihood Estimation (M.L.E.) give for the parameter p of a geometric distribution? For a geometric random variable X, counting the number of trials until the first success, and probability of success p on each independent and identical trial, the probability mass function (PMF) is f(x) = p*(1-p)^(x-1). The likelihood function takes a random sample x1, x2, ..., xn and multiplies these PMF values to get L(p) = f(x1)*f(x2)*...*f(xn). It is easier to maximize the log-likelihood function LL(p) = ln(L(p)) because the products get converted to summations. In the end, we get the estimator p̂ = 1/X̄ after taking the derivative, setting it equal to zero, and solving for the critical point for p. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.