1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
|
ex1 <- function(total = 24, marked = 4, boxes = 4, iterations = 10000) {
perbox <- total %/% boxes
successes <- 0
for (i in 1:iterations) {
apples <- sample(append(rep("marked", each=marked), rep("normal", each=total - marked)))
current <- 0
for (b in 0:boxes-1) {
current <- current + (1 == sum(apples[1:perbox + b*perbox] == "marked"))
}
successes <- successes + (current == 4)
}
return (round(successes / iterations, digits=2))
}
ex1()
ex2 <- function(n, lambda = 1/5, N = 10000, mu = 5, sigma = 5 / sqrt(n)) {
x <- function() rexp(n, rate=lambda)
xdash <- replicate(N, sum(x()) / n)
fchapeau <- function(t) {
# I е излишна на практика, но гледам да следвам условието възможно най-стриктно
I <- function(a) as.integer(a == TRUE)
return (1/N * sum(I(xdash <= t)))
}
t <- seq(2, 8, by=0.1)
Fpoints <- sapply(t, fchapeau)
Npoints <- sapply(t, function(t) pnorm(t, mu, sigma))
plot (t, Fpoints, type="l")
lines(t, Npoints, lty=2, col="darkred")
}
ex2(30)
ex2(120)
ex2(200)
|
