I generated 200 random numbers with the random variable that Y~Exponential(0.8) using:
n=rexp(200,0.8)
bins=cut(n,breaks=c(0,1,2,3,max(n)))
I am trying to compute the expected number of counters for each bin knowing that Y~Exponential(0.8). How can i do this?
You can use the same set of functions that ?rexp is from to calculate the proportions in each range, and use this to calculate expected numbers:
num <- 200
brks=c(0,1,2,3,Inf)
set.seed(12345)
n <- rexp(num,0.8)
bins <- cut(n,breaks=brks)
expect.prop <- diff(pexp(brks, rate=0.8))
#[1] 0.55067104 0.24743245 0.11117856 0.09071795
rbind(
observed=table(bins),
expected=num*expect.prop
)
# (0,1] (1,2] (2,3] (3,Inf]
#observed 115.0000 42.00000 24.00000 19.00000
#expected 110.1342 49.48649 22.23571 18.14359
