9/7/2020

Complete our Problem Session for Chapter 14 exercises

• 14.27 - Meg
• 14.28 - Andrew

Chapter 15 Random Variables

• Discrete versus continuous random variables
• Cumulative distribution function (c.d.f.) - F(x) = P(X<=x)
• Empirical c.d.f. - F-hat(x) = (# of observations <=x)/n
• Expected value
• Variance
• Standard deviation
• WLLN
• Sample proportion - p-hat

Chapter 3 (will be discussed on Wednesday)

• Notational conventions
  • Variables - simple variables, vectors, matrices, and arrays
  • Objects - variables and user-definied functions
• Branching with if and if-else --- syntax matters, be careful
• sums - with loops or sum(x)
• products - with loops or prod(1:n) or factorial(n)
• Memory use - changing the size of an array takes time
  • preallocation - creating a vector
  • redimensioning - changing the size of a vector
• While loops - used when we do not know how many times we will need to execute a loop
• Vector based programming - vector opearations are more efficient than looping
• ifelse - very powerful function - e.g., ifelse(x>0, "Pos", "Neg")
• pmin() and pmax() are vectorized versions of min() and max()
  • e.g., pmin(c(1,2,3), c(3,2,1), c(2,2,2))
• Program flow - charting the flow of a program is extremely helpful for verifying your logic (i.e., is the program doing what you want?) and finding errors in your code.
• Debugging
  • Tip 1 - Use cat() to examing values of your variables at various stages throughout your program
  • Tip 2 - Use the KISS principle
  • Tip 3 - Use dry runs where you know the answer to test your code

Please read Chapters 3 and 16 for class on Wednesday