Tag: R Language

R Simulation – Monty Hall Problem

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice? (taken from Wikipedia)

Shall I change doors or stick to my original choice? That is the question! Let’s write an R Script to run a simulation for this problem…

```
# Monty Hall problem simulation
```
```
 
```
```
print("Monty Hall problem simulation")
```
```
print("-----------------------------")
```
```
 
```
```
# define variables
```
```
win.switch.count <- 0
```
```
win.noswitch.count <- 0
```
```
sim.count <- 50000
```
```
switch.count <- 0
```
```
noswitch.count <- 0
```
```
 
```

print(paste("Running", sim.count, "simulations"))

```
 
```
```
# run simulation for x times
```
```
for (i in 1:sim.count) {
```

    # create doors, a vector 1 to 3, for door 1, door 2, and door 3

```
    doors <- c(1, 2, 3)
```
```
 
```
```
    # set price behind a random door
```
```
    price.door <- sample(1:3, 1)
```
```
 
```
```
    # the guest picks up a random door
```
```
    guest.door <- sample(1:3, 1)
```
```
 
```

    # monty needs to open a door where there is a goat

```
 
```

    # monty door is not price and is not guest

```
    doors[price.door] <- 0
```
```
    doors[guest.door] <- 0
```
```
 
```

    # monty choose the max() door from the resultant vector

```
    monty.door <- max(doors)
```
```
 
```

    # re-insert the price door back in list!!

```
    doors[price.door] <- price.door
```
```
 
```

    # pick a number from 1 to 10 and if it is 5 or less, guest will switch door

```
    if (sample(1:10, 1) < 6) {
```
```
        # guest switch choice
```
```
        doors[monty.door] <- 0
```

        # since we are neutralising the vector and leaving only the only door not

```
        # chosen by the guest or monty
```

        # the sum of doors will be the door left

```
        guest.door <- sum(doors)
```

        switch.count <- switch.count + 1

```
        if (price.door == guest.door) {
```

            win.switch.count <- win.switch.count + 1

```
        }
```
```
    } else {
```
```
        # no switch
```

        noswitch.count <- noswitch.count + 1

```
        if (price.door == guest.door) {
```

            win.noswitch.count <- win.noswitch.count + 1

```
        }
```
```
    }
```
```
}
```
```
 
```
```
# display output
```

probability.switch <- win.switch.count / switch.count

probability.noswitch <- win.noswitch.count / noswitch.count

print(paste("P(switch door) =", probability.switch))

print(paste("P(no switch) =", probability.noswitch))

print(paste("Check P(switch) + P(no switch) =", probability.switch + probability.noswitch))

Answer:

Running the script returns something similar to:

[1] "Monty Hall problem simulation"
[1] "-----------------------------"
[1] "Running 50000 simulations"
[1] "P(switch door) = 0.671743823458863"
[1] "P(no switch) = 0.332786360361803"
[1] "Check P(switch) + P(no switch) = 1.00453018382067"
>

Switching increase the chance to win!

For a mathematical explanation we suggest to watch Numberphile’s video at https://www.youtube.com/watch?v=4Lb-6rxZxx0.

April 6, 2016

R Characters
In today’s blog we take a look at string in R. Strings in R are represented by character objects.
Let’s keep Clounce in a variable:
> name <- "Clounce"
Now let’s print it on screen:
> print(name) [1] "Clounce"
Numbers can be converted to characters using the as.character function. Let’s look at an example:
> x <- as.character(pi) > x # print the value of x [1] "3.14159265358979" > class(x) # print the class name of x [1] "character"
Characters can be concatenated by the paste() function.
> name <- "Clounce" > description <- "the best!" > paste(name, description) [1] "Clounce the best!"
Note that the paste() functions adds a space between the two variables. Cool eh!
Three common functions associated with strings are sprintf(), substr(), and sub(). Let’s look at each function separately.
sprintf() is useful to display data. It has the same C equivalent syntax.
> sprintf("I am %s. I like %f", name, pi) [1] "I am Clounce. I like 3.141593"
To get part of a string, use substr(). Note that it takes the start and stop position of the text you want to extract. The first character has position 1.
> sentence <- paste(name, description) > substr(sentence, start = 9, stop = 11) [1] "the" >
Replacing part of string can be done using the sub() function.
> sentence [1] "Clounce the best!" > sub("best", "great", sentence) [1] "Clounce the great!" >
February 27, 2016

Tag: R Language

R Simulation – Monty Hall Problem

Answer:

R Characters