Probability & Statistics Exam 2 Review Problems & Solutions (includes Maximum Likelihood Estimation)

https://www.youtube.com/watch?v=1Q7ALcwT97A. Probability and Statistics Exam Review Types of Problems: 1) Continuous Random Variables, including Normal, Exponential, and Chi-Square, 2) Bivariate Random Variables (Discrete & Continuous), Joint, Marginal, and Conditional Densities, 3) Descriptive Statistics, 4) Method of Moments, 5) Maximum Likelihood Estimation, 6) Actuarial Science (Net Single Premium (NSP) based on force of interest and survival function). https://amzn.to/3Hd7tFN ("Probability and Statistics with Applications, a Problem-Solving Text") This is for a Calculus-based Probability and Statistics Course for Scientists and Engineers. Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinneymath?sub_confirmation=1 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: https://twitter.com/billkinneymath 🔴 Follow me on Instagram: https://www.instagram.com/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/ (0:00) Types of problems (0:43) Continuous Random Variable: find a PDF, a CDF, a probability, mean, variance, and standard deviation. (9:08) Normal distribution problem (find a probability and a percentile) (14:09) Discrete bivariate random variable (tabular data for the joint probability mass function, joint PMF). Find marginal densities and probabilities. (17:28) First moment and covariance. X and Y are not independent. (21:05) Conditional distribution values (conditional probability mass function PMF) (24:08) Continuous bivariate joint random variable. Find a marginal density, confirm the joint distribution is a probability density function. (27:52) Curve of regression given a conditional density (30:37) Find & interpret the curve of regression at a point (32:48) Normal approximation to binomial distribution (38:46) Chi-Square probability and critical value (40:54) Method of Moments estimator for Geometric Random Variable parameter p. (44:38) Double stem-and-leaf diagram (stemplot). It is right-skewed. (47:53) Boxplot for five-number summary (box and whisker plot) (52:11) Unbiased estimates for mean and variance (observed values of unbiased estimators) (54:49) Find maximum likelihood estimate for the mean of an exponential distribution (based on being told the maximum likelihood estimator). (56:15) Derive maximum likelihood estimator for the mean an exponential distribution (maximize the likelihood function by maximizing the log likelihood function). (1:03:40) Survival random variable with given survival function. Find a probability using the survival function. (1:05:10) Find force of mortality (use the survival function) (1:07:01) Darth Vader rule to find the mean (1:09:15) Find Net Single Premium (and interpret). Use a given interest rate to convert to a force of interest before integrating. AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.