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38 lines
607 B
Plaintext
38 lines
607 B
Plaintext
# Exercise 9 : Estimation of Pi
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## Methode 1
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```{r}
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n <- 150000
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pi_1 <- function(n) {
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U <- runif(n, 0, 1)
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return(4 / n * sum(sqrt(1 - U^2)))
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}
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pi_1(n)
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```
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## Methode 2
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```{r}
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n <- 150000
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pi_2 <- function(n) {
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U1 <- runif(n, 0, 1)
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U2 <- runif(n, 0, 1)
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return(4 / n * sum(U1^2 + U2^2 <= 1))
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}
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pi_2(n)
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```
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## Best Estimator
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```{r}
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n <- 1000
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m <- 150000
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sample_1 <- replicate(n, pi_1(m))
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sample_2 <- replicate(n, pi_2(m))
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cat(sprintf("[Methode 1] Mean: %s. Variance: %s \n", mean(sample_1), var(sample_1)))
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cat(sprintf("[Methode 2] Mean: %s. Variance: %s", mean(sample_2), var(sample_2)))
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```
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