Problem Set 2: Problem 3

Start with pseudocode

Toss a coin, multiple times. Count the number of tosses required to get to 100 heads.

You should be using a while loop for this.

Start pseudo coding

start a head counter start a toss counter

while my head counter < 100 toss_coin <- uniform random variable from 0 to 1, assign > 0.5 as a heads check if it’s heads if it’s heads, then add 1 to my heads counter if it’s not head (tails), don’t do anything add 1 to my toss counter

how many tosses how many heads

Coin_Flip <- function(){
  Coin <- runif(1)
  if (Coin > 0.5) {
    Results <- "Heads"
  } else {
    Results <- "Tails"
  }
  return(Results)
}

Coin_Flip()

## [1] "Heads"

head_count <- 0
flip_count <- 0

while(head_count < 100){
  if(Coin_Flip() == "Heads"){
    head_count <- head_count + 1
  }
  flip_count <- flip_count + 1
}

print(head_count)

## [1] 100

print(flip_count)

## [1] 193

Skip the intuitive Coin_Flip function

head_count <- 0
flip_count <- 0

while(head_count < 100){
  if(runif(1) > 0.5){
    head_count <- head_count + 1
  }
  flip_count <- flip_count + 1
}

print(head_count)

## [1] 100

print(flip_count)

## [1] 190

Use sample instead

head_count <- 0
flip_count <- 0

while(head_count < 100){
  coin_toss <- sample(x = c("Heads","Tails"), size = 1, replace = TRUE)
  if(coin_toss == "Heads"){
    head_count <- head_count + 1
  }
  flip_count <- flip_count + 1
}

print(head_count)

## [1] 100

print(flip_count)

## [1] 199

head_count <- 0
tail_count <- 0

while(head_count < 100){
  ifelse(runif(1) > 0.5, yes = (head_count <- head_count + 1), no = (tail_count <- tail_count + 1))
}

print(head_count)

## [1] 100

print(head_count + tail_count)

## [1] 217

Arctic fox - red fox problem

attacker <- “red fox” red_fox_wins <- 0 arctic_fox_wins <- 0

draw a random value for the attack outcome

while red_fox_wins < 21 or arctic_fox_wins < 21 if attacker == red fox if rand val is <= 0.6 red fox wins increase number of red_fox_wins attacker <- “red fox” else rand val > 0.6 arctic fox wins increase number of arctic_fox_wins attacker <- “arctic fox”

if attacker == arctic fox if rand val is <= 0.5 red fox wins increase number of red_fox_wins attacker <- “red fox” else rand val > 0.5 arctic fox wins increase number of arctic_fox_wins attacker <- “arctic fox”

attacker <- sample(c("red fox", "arctic fox"), size = 1)
red_fox_wins <- 0
arctic_fox_wins <- 0

while(red_fox_wins < 21 & arctic_fox_wins < 21){
  if(attacker == "red fox"){ 
    if( runif(1) <= 0.6){
      print("red fox wins bout")
      red_fox_wins <- red_fox_wins + 1
      attacker <- "red fox"
    } else {
      print("arctic fox wins")
      arctic_fox_wins <- arctic_fox_wins + 1
      attacker <- "arctic fox"
    }
  } else if(attacker == "arctic fox"){ 
    if( runif(1) <= 0.5){
      print("red fox wins bout")
      red_fox_wins <- red_fox_wins + 1
      attacker <- "red fox"
    } else {
      print("arctic fox wins")
      arctic_fox_wins <- arctic_fox_wins + 1
      attacker <- "arctic fox"
    }
  }
}

## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "arctic fox wins"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "arctic fox wins"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "arctic fox wins"
## [1] "arctic fox wins"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "arctic fox wins"
## [1] "arctic fox wins"
## [1] "arctic fox wins"
## [1] "arctic fox wins"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "red fox wins bout"
## [1] "arctic fox wins"
## [1] "arctic fox wins"
## [1] "red fox wins bout"
## [1] "red fox wins bout"