# Exercice 1 : Uniform

```{r}
n <- 10e4
U <- runif(n)
X <- 5 * (U <= 0.4) + 6 * (0.4 < U & U <= 0.6) + 7 * (0.6 < U & U <= 0.9) + 8 * (0.9 < U)
barplot(table(X)/n)
```

# Exercice 3 : Box Muller Algo

```{r}
BM <- function(n) {
  U1 <- runif(n)
  U2 <- runif(n)
  X1 <- sqrt(-2 * log(U1)) * cos(2 * pi * U2)
  X2 <- sqrt(-2 * log(U1)) * sin(2 * pi * U2)
  return(c(X1, X2))
}

n <- 10e4
X <- BM(n)

hist(X, breaks = 100, freq = FALSE)
curve(dnorm(x), add = TRUE, col = "red")
```