Properties of expectation

Description:

• Chapter 7.4 in “a first course in probability and statistics”

Properties of expectation:

• If $P(a\le x\le b)=1$, then $a\le E[X]\le b$
• If $X>Y$ for all outcomes, then $E[X]>E[Y]$
• If $E[X_i]$ is finite for all $i=1,...,n$ then $E[X_1+...+X_n]=E[X_1]+...+E[X_n]$
• If $X$ and $Y$ are independent, then, for any functions $h$ and $g$, $E[g(X).h(Y)]=E[g(X)].E[h(Y)]$

Covariance and Correlation

Conditional expectation

Indicator Variable

Conditional variance

Prediction

---