Density and cumulative density

Foundations of Probability in R

David Robinson

Chief Data Scientist, DataCamp

Simulating many outcomes

$$X \sim \text{Binomial}(10, .5)$$

$$\Pr(X=5)$$

flips <- rbinom(100000, 10, .5)

flips <- rbinom(100000, 10, .5)

flips == 5
# [1] FALSE TRUE FALSE FALSE...

mean(flips == 5)
# [1] 0.2463

dbinom(5, 10, .5)
# [1] 0.2460938

dbinom(6, 10, .5)
# [1] 0.2050781

dbinom(10, 10, .5)
# [1] 0.0009765625

$$X \sim \text{Binomial}(10, .5)$$

$$\Pr(X\leq 4)$$

flips <- rbinom(100000, 10, .5)
mean(flips <= 4)
# [1] 0.37682

pbinom(4, 10, .5)
# [1] 0.37695

Foundations of Probability in R