Lecture 1: Probability and Counting | Statistics 110
46:29Lecture 2: Story Proofs, Axioms of Probability | Statistics 110
45:40Lecture 3: Birthday Problem, Properties of Probability | Statistics 110
48:54Lecture 4: Conditional Probability | Statistics 110
49:45Lecture 5: Conditioning Continued, Law of Total Probability | Statistics 110
50:01Lecture 6: Monty Hall, Simpson's Paradox | Statistics 110
49:00Lecture 7: Gambler's Ruin and Random Variables | Statistics 110
51:45Lecture 8: Random Variables and Their Distributions | Statistics 110
50:24Lecture 9: Expectation, Indicator Random Variables, Linearity (STAT 110)
50:23Lecture 10: Expectation Continued (STAT 110)
50:10Lecture 11: The Poisson Distribution (STAT 110)
42:46Lecture 12: Discrete vs. Continuous, the Uniform (STAT 110)
49:56Lecture 13: Normal Distribution (STAT 110)
51:10Lecture 14: Location, Scale, and LOTUS (STAT 110)
48:55Lecture 16: Exponential Distribution (STAT 110)
18:19Lecture 17: Moment Generating Functions (STAT 110)
50:45Lecture 18: MGFs Continued (STAT 110)
49:41Lecture 19: Joint, Conditional, and Marginal Distributions (STAT 110)
50:09Lecture 20: Multinomial and Cauchy (STAT 110)
49:00Lecture 21: Covariance and Correlation (STAT 110)
49:26Lecture 22: Transformations and Convolutions (STAT 110)
47:46Lecture 22: Transformations and Convolutions (STAT 110)
This lecture explores transformations of random variables (change of variables) and introduces the LogNormal distribution. It covers convolutions for sums of variables and demonstrates how probability can be used to prove existence.
We discuss transformations of r.v.s (change of variables), the LogNormal distribution, and convolutions (sums). As a bonus, we show how in certain problems one can use probability to prove existence.