Hello, i have this excersice in R studio Write a function in R that generates simulations...

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Hello, i have this excersice in R studio

Write a function in R that generates simulations of a Poisson random variable as follows: define I = [Î»], and use p_i + 1 = Î»p_i / (i + 1) to determine F recursively. Generate a random number U, determine if Xâ‰¤I by comparing if Uâ‰¤F (I). If Xâ‰¤I searches downwards starting at I, otherwise it searches upwards starting from I + 1. Compare the time it takes for the two algorithms in 5000 simulations of a Poisson random variable with parameter Î» = 10,200,500.

example

# Poisson usando InversiÃ³nrpoisI <- function(lambda = 1){ U <- runif(1) i <- 0 p <- exp(-lambda) P <- p while(U >= P){  p <- lambda * p / (i + 1)  P <- P + p  i <- i + 1 } i}sims_pois <- rerun(2000, rpoisI()) %>% flatten_dbl()ggplot() +  geom_histogram(aes(x = sims_pois, y = ..density..), binwidth = 1)

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# Poisson Random generator

### Compare the time it takes for the two algorithms in 5000 simulations of
#Â Â a Poisson random variable with parameter Î» = 10,200,500.
poisn.gen=function(lambda,size){
x=NULL
for (j in 1:size) {
Â Â Â u=runif(1)
Â Â Â p=exp(-lambda)
Â Â Â f=p
Â Â Â i=0
Â Â Â s=0
Â Â Â while(s==0){
Â Â Â Â Â if(u Â Â Â Â Â Â Â x=append(x,i,after = length(x))
Â Â Â Â Â Â Â s=1
Â Â Â Â Â }
Â Â Â Â Â else{
Â Â Â Â Â Â Â p=(p*lambda)/(i+1)
Â Â Â Â Â Â Â f=f+p
Â Â Â Â Â Â Â i=i+1
Â Â Â Â Â }
Â Â Â }
}
return(x)
}
poisn.gen(10,5000)

poisn.gen(200,5000)

poisn.gen(500,5000)

hist(poisn.gen(500,5000))

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