Question

Please provide the code in the language R. (请提供语言R的代码)

Suppose the incubation period, T , of a certain disease can be modeled by an exponential distribution with a mean of 4.5 days

1. Run a simulation to estimate the probability that, among 100 people who have contracted the disease, 80 or more people will develop symptoms within 5 days.

2. Suppose the number of new cases contracting the disease today follows a Poisson distribution with a mean of 100 people. Modify your simulation in (1) to estimate the probability that, among people who have contracted the disease today, 80 or more people will show symptoms within 5 days.

3. Generate a histogram of the distribution of the number of people that will show symptoms within 5 days, under the setup in (2).

Answer 1

1.

R code:

n=100000
a=0
count=0

for(k in 1:n)
{
   for(i in 1:100)
   {
       x=rexp(100,(1/4.5))
       if(x[i]<5)a=a+1
   }
   if(a>80)count=count+1
   a=0
}

cat("The required probability is ",count/n)

Result:

[1] The required probability is 0.00151

2.

R code:

n=100000
a=0
count=0

x=rpois(n,100)
y=rexp(n,1/4.5)
for(i in 1:n)
{

   if(x[i]>80 && y[i]<5 ) count=count+1

}

cat("The required probability is",count/n,"\n")

Result:

The required probability is 0.65526

3.

R code:

n=10000
k=1
z=c()

x=rpois(n,100)
y=rexp(n,1/4.5)
for(i in 1:n)
{

   if(y[i]<5)
   {
       z[k]=x[i]
       k=k+1
   }

}

hist(z)
Graph: