Random Number Generation

🎲 The Magic Number Machine: Random Numbers in R

The Story of Randomness

Imagine you have a magical dice machine. Every time you press a button, it gives you a number you can’t predict. That’s exactly what random number generation is in R!

But here’s the twist: computers aren’t actually random. They use clever math tricks to pretend to be random. And sometimes, we WANT to control this “fake randomness” so we can repeat our experiments.

🌱 Part 1: The Magic Seed (Random Seed Setting)

What is a Seed?

Think of planting a flower. If you plant the same seed in the same pot with the same water, you get the same flower every time.

R’s random number generator works the same way!

# Plant the seed
set.seed(42)

# Now pick a random number
runif(1)
# Result: 0.9148060

Run it again:

set.seed(42)
runif(1)
# Result: 0.9148060

Same seed = Same “random” number!

Why Do We Need Seeds?

The Magic of set.seed()

# Any number works as a seed
set.seed(123)
runif(3)
# [1] 0.288 0.788 0.409

set.seed(999)
runif(3)
# [1] 0.388 0.685 0.003

Different seeds = Different sequences!

Real-World Example: Fair Experiment

# Your friend wants to check your work
set.seed(2024)

# Generate 5 random test scores
scores <- round(runif(5, 60, 100))
print(scores)
# [1] 83 72 95 68 89

# Your friend runs the same code
# They get EXACTLY the same scores!

🎯 Part 2: Random Sampling (Picking Things Randomly)

The Lottery Ball Machine

Imagine a machine with numbered balls. You reach in and grab some without looking. That’s sample() in R!

# 10 balls numbered 1-10
# Pick 3 without looking
sample(1:10, 3)
# Result: 7 2 9 (varies each time)

Two Ways to Sample

graph TD
    A["🎱 Sampling"] --> B["Without Replacement"]
    A --> C["With Replacement"]
    B --> D["Each item picked once"]
    B --> E["Like lottery balls"]
    C --> F["Items can repeat"]
    C --> G["Like dice rolls"]

Without Replacement (Default)

Once you pick a ball, it’s gone:

# Pick 3 students from class of 5
students <- c("Amy", "Bob", "Cat", "Dan", "Eve")
sample(students, 3)
# [1] "Cat" "Amy" "Eve"

# No one is picked twice!

With Replacement

Put the ball back after each pick:

# Roll a dice 10 times
sample(1:6, 10, replace = TRUE)
# [1] 3 6 1 3 4 2 6 5 3 1

# Numbers CAN repeat (like real dice)

The Complete Recipe

sample(
  x = items_to_pick_from,
  size = how_many_to_pick,
  replace = TRUE_or_FALSE,
  prob = weights_for_each_item
)

Weighted Sampling: Unfair Dice!

What if some options should appear more often?

# Unfair coin: 70% heads, 30% tails
sample(
  c("Heads", "Tails"),
  size = 10,
  replace = TRUE,
  prob = c(0.7, 0.3)
)
# [1] "Heads" "Heads" "Tails" "Heads"...

Shuffling: Random Order

# Shuffle a deck (just first 5 cards)
cards <- c("Ace", "King", "Queen", "Jack", "10")
sample(cards)
# [1] "Queen" "10" "Ace" "Jack" "King"

# Same cards, random order!

🔗 Combining Seeds + Sampling

The real power comes when you combine them:

# Reproducible random sample!
set.seed(777)
lucky_winners <- sample(1:1000, 3)
print(lucky_winners)
# [1] 234 891 456

# Anyone with seed 777 gets
# the SAME three winners!

🎮 Quick Reference

🌟 Key Takeaways

1. Seeds are magic keys - Same seed = Same random numbers
2. Use set.seed() before randomness - Makes experiments repeatable
3. sample() is your lottery machine - Pick items randomly
4. replace=TRUE - Put items back (can repeat)
5. replace=FALSE - Don’t put back (no repeats)
6. prob weights - Make some options more likely

🚀 You’re Ready!

You now understand how R creates “controlled randomness.” Whether you’re:

• Running a scientific simulation
• Picking random survey respondents
• Shuffling a playlist
• Testing your code

You have the tools to make it random AND reproducible!

Remember: In R, randomness is your friend - especially when you can control it with seeds!