Densities

This is the (small) population of patients with a rare disease, along with where they live:

Name	City
Nana	Alpharetta
Nia	Alpharetta
Anya	Alpharetta
Yamiaya	Atlanta
Youssef	Atlanta
Ibrahim	Alpharetta
Lizelle	Buckhead
Chen	Atlanta
Carlos	Buckhead
Jin	Buckhead
Rachael	Alpharetta
Lukas	Alpharetta
Olivia	Atlanta
Ayesha	Buckhead
Fatima	Buckhead

A) Come up with the density R function for "city " in this population.

B. The function (equivalent to or) that draws samples from a "population" that has a variable X that has this density. You don't have to understand how this code works, but if you're curious, all it does is pick a number between 1 and 3 and depending on what it is it samples from one of three different normal distributions.

r_mydensity=function(n){ df = tibble(

S = sample(1:3, size=n, replace=T),

X = case_when(

S==1~rnorm(n,mean=-5,sd=1), S==2 ~ rnorm(n, mean = 0, sd = 2), S==3~rnorm(n,mean=5,sd=1.5)

)

) %>% pull(X)

}

sample = r_mydensity(1000)

hist(sample)