diff --git a/lectures/lecture10/lecturenotes.tex b/lectures/lecture10/lecturenotes.tex index 8e2c5523afc5ab8b3afa77a9747e47a7a7c67702..710f9f9c471ec3ee350e9c17a859d91a6fced777 100644 --- a/lectures/lecture10/lecturenotes.tex +++ b/lectures/lecture10/lecturenotes.tex @@ -33,6 +33,7 @@ \2 \textit{Why do we consider our measurements random variables?} \2 CDF vs. PDF vs. PMF \2 \textit{How do we calculate probability a value will be within a range?} + \3 Integral (CDF) at point $b$, minus integral at point $a$ \1 Important probability concept: Expectation \2 The value you can expect to get'' @@ -44,11 +45,12 @@ \2 $E[XY]$ is expected value of $X * Y$ \2 Linearity of expectation - \1 Mean, median, mode \2 \textit{When to use each} \2 Categorical: mode, total: mean, skewed: median, else: mean \2 Additive (arithmetic), multiplicative (geometric), harmonic + \2 Mistakes with means: large range, skewness, multiplying when not + independent, ratio with different bases \1 Covariance \2 Measure whether two random variables vary together