Class 6

Example 1

\[ y = \ln(x^2) \]

ln_sq <- function(z){
  y <- log(z^2)
  return(y)
}
ln_sq(34)

[1] 7.052721

Example 2

\[ f(x) = \left\{\begin{array}{cc} x^3 & x<0\ \\ x^2 + 5 & \mathrm{otherwise} \end{array} \right. \]

secondfunction <- function(x){
  if(x<0){
    y = x^3
  } else{
    y = x^2 +5
  }
  return(y)
}
secondfunction(-1)

[1] -1

secondfunction(1)

[1] 6

Example 3

\[ f(x,y) = \left\{\begin{array}{cc} x^3 e^y & x<0\ \\ x^2 + 5 + \ln(y) & \mathrm{otherwise} \end{array} \right. \]

this <- function(x, y) {
  if(y < 0) {
    stop("it is negative")
  }
  if(x < 0) {
    z <- x^3 * exp(y)
  } else {
    z <- x^2 + 5 + log(y)
  }
  return(z)
}
this(2,1)

[1] 9

this(-2,1)

[1] -21.74625

this(2,-1)

Error in this(2, -1) : it is negative

Example 4

\[ z = \frac{x-\bar y}{\sqrt{s^2_{y}/n_y}} \]

zscore <- function(x,y){
  (x-mean(y))/(sqrt(var(y)/length(y)))
}
zscore(5,1:5)

[1] 2.828427