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40 lines
557 B
Plaintext
40 lines
557 B
Plaintext
# Exercise 10 : Integral Calculation.
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## Estimation of δ using the classical Monte Carlo
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### Uniform + Normal distributions
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```{r}
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n <- 10e4
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X <- runif(n, 0, 5)
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Y <- rnorm(n, 0, sqrt(2))
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Y[Y <= 2] <- 0
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h <- function(x, y) {
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5 *
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sqrt(pi) *
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sqrt(x + y) *
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sin(y^4) *
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exp(-3 * x / 2)
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}
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I1 <- mean(h(X, Y))
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I1
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```
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### Exponential + Normal distributions
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```{r}
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n <- 10e4
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X <- runif(n, 0, 5)
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Y <- rexp(n, 3 / 2)
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Y[Y <= 2] <- 0
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X[X <= 5] <- 0
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h <- function(x, y) {
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4 / 3 * sqrt(pi) * sqrt(x + y) * sin(y^4)
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}
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I2 <- mean(h(X, Y))
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I2
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``` |