STA256 Lecture 16

• Statistical Independence
• Independent Random Vectors
• Hints for STA256 Quiz 4
  • Review Jensen's Inequality
  • Calculate probability for Random Vectors
  • Transformations - Bivariate
    • Be careful with support
  • #tk
• Example:
  • $\begin{array}{ccc}& & x_1\\ & & 0& 1\\ x_2& 1& 0.25& 0.25\\ & 2& 0.25& 0.25\end{array}$
  • How do you find $E[x_1{x}_2]=?$
  • $y=x_1{x}_2$
  • $\begin{array}{ccc}{x}_1& x_2& y=x_1{x}_2\\ 0& 1& 0\\ 0& 2& 0\\ 1& 1& 1\\ 1& 2& 2\end{array}$
  • $\{\begin{array}{ll}P(Y=0)& =P(X_1=0,X_2=1)+P(X_1=0,X_2=2)\\ & =0.25+0.25=0.5\\ P(Y=1)& =\dots \\ P(Y=2)& =\dots \end{array}$
  • #tk
• Correlation and Covariance
• Correlation