HarvardX PH125.1x: Chapter 3 Exercises

Section 3.6

1. What will this conditional expression return?

x <- c(1, 2, -3, 4)

if(all(x>0)){
  print("All Positives")
} else {
  print("Not all positives")
}

## [1] "Not all positives"

2. Which of the following expressions is always FALSE when at least one entry of a logical vector x is TRUE?

x<-c(TRUE, FALSE, TRUE)
y<-c(TRUE, FALSE, FALSE)
z<-c(TRUE, TRUE, TRUE)
all(x)

## [1] FALSE

any(x)

## [1] TRUE

any(!x)

## [1] TRUE

all(!x)

## [1] FALSE

all(!y)

## [1] FALSE

all(!z)

## [1] FALSE

3.  The function nchar tells you how many characters long a character vector is. Write a line of code that assigns to the object new_names the state abbreviation when the state name is longer than 8 characters.

library(dslabs)
data("murders")
longst<- function(j){
  new_names<-ifelse(nchar(j)>8, murders$abb, murders$state)
    }
pizza<-longst(murders$state)
pizza

##  [1] "Alabama"  "Alaska"   "Arizona"  "Arkansas" "CA"       "Colorado"
##  [7] "CT"       "Delaware" "DC"       "Florida"  "Georgia"  "Hawaii"  
## [13] "Idaho"    "Illinois" "Indiana"  "Iowa"     "Kansas"   "Kentucky"
## [19] "LA"       "Maine"    "Maryland" "MA"       "Michigan" "MN"      
## [25] "MS"       "Missouri" "Montana"  "Nebraska" "Nevada"   "NH"      
## [31] "NJ"       "NM"       "New York" "NC"       "ND"       "Ohio"    
## [37] "Oklahoma" "Oregon"   "PA"       "RI"       "SC"       "SD"      
## [43] "TN"       "Texas"    "Utah"     "Vermont"  "Virginia" "WA"      
## [49] "WV"       "WI"       "Wyoming"

4. Create a function sum_n that for any given value,  n  , computes the sum of the integers from 1 to \(n\) (inclusive). Use the function to determine the sum of integers from 1 to 5,000.

sum_n<-function(n){
      s<-seq(1, n, 1)
      j<-sum(s)
      return(j)
}
sum_n(5000)

## [1] 12502500

5. Create a function altman_plot that takes two arguments, x and y, and plot the difference against the sum.

altman_plot<-function(x, y){
  j<-plot(x-y, x+y)
  return(j)
}
altman_plot(6, 1)

## NULL

6. After running the code below, what is the value of x?

x<-3
my_func<-function(y){
  x<-5
  y+5
}
x

## [1] 3

7. Write a function compute_s_n that for any given \(n\) computes the sum \(S_n=1^2+2^2+3^2+...+n^2\) Report the value of the sum when \(n=10\).

compute_s_n<-function(n){
  love<-seq(1, n, 1)
  pyar<-love^2
  ishq<-sum(pyar)
  return(ishq)
}
compute_s_n(10)

## [1] 385

8. Define an empty numerical vector s_n of size 25 using s_n <-vector("numeric", 25) and store in the results of \(S_1, S_2, S_{25}\)

m<-25
s_n<-vector("numeric", 25)
for(i in 1:m){
  s_n[i]<-compute_s_n(i)
}
s_n

##  [1]    1    5   14   30   55   91  140  204  285  385  506  650  819 1015 1240
## [16] 1496 1785 2109 2470 2870 3311 3795 4324 4900 5525

9. Repeat exercise 8, but this time use sapply.

x<-1:25
s_n<-sapply(x, compute_s_n)
s_n

##  [1]    1    5   14   30   55   91  140  204  285  385  506  650  819 1015 1240
## [16] 1496 1785 2109 2470 2870 3311 3795 4324 4900 5525

10. Repeat exercise 8, but this time use mapply.

crab<-seq(1, 25, 1)
mapply(compute_s_n, crab)

##  [1]    1    5   14   30   55   91  140  204  285  385  506  650  819 1015 1240
## [16] 1496 1785 2109 2470 2870 3311 3795 4324 4900 5525

11. Plot \(S_n\) versus \(n\). Use points defined by \(n=1,…,25\).

n<-seq(1, 25, 1)
plot(n, s_n)

12. Confirm that the formula for this sum is \(S_n=n(n+1)(2n+1)/6\)

n<-seq(1,25, 1)
j<-n*(n+1)*(2*n+1)/6
identical(j, s_n)

## [1] TRUE