Solutions des TPs
659
curve(-8 * x+4,add=TRUE)
# Densit´ e sur [0,0.5] : f(x)=-8x+4
D- Vers la notion de mod´ elisation
10.1- X <- function() ifelse(rbinom(1,1,0.5),"PILE","FACE")
X()
10.2- lancer.le.d´ e <- function() sample(1:6,1)
lancer.le.d´ e()
10.3- yams <- function() sample(1:6,size=5,replace=TRUE)
10.4- n <- 1000000
result <- replicate(n,yams(),TRUE)
test <- function(res) ifelse(length(unique(res))> 1,0,1)
prop <- mean(apply(result,MARGIN=2,FUN=test))
E- Th´ eor` eme de Box et Muller
10.1- n <- 1000
u1 <- runif(n)
u2 <- runif(n)
z1 <- sqrt(-2 * log(u1)) * cos(2 * pi * u2)
z2 <- sqrt(-2 * log(u1)) * sin(2 * pi * u2)
10.2- Estimation non param´ etrique de la densit´ e :
require("MASS")
ngrid <- 40
denobj<-kde2d(z1,z2,n=ngrid)
den.z <-denobj$z
10.3- Surface de densit´ e de la normale bivari´ ee :
require("rgl")
xgrid <- denobj$x
ygrid <- denobj$y
bi.z <- dnorm(xgrid)% * %t(dnorm(ygrid))
Nouvelle fenˆ etre :
open3d()
bg3d(color="#887777")
light3d()
Repr´ esentation des donn´ ees simul´ ees :
spheres3d(z1,z2,rep(0,n),radius=0.1,color="#CCCCFF")