v1 <- v2 <- c()
for (i in 1:200){
v1[i] <- prob.nd(n = i, nd = 1, k = 1, p_tie = 0.1)
v2[i] <- prob.nd(n = i, nd = 1, k = 1, p_tie = 0.1)
}
# > prob.nd(n = 5, nd = 5, k = 0, p_tie = 0)
# [1] 0.03125
# > prob.nd2(n = 5, nd = 5, k = 0, p_tie = 0)
# [1] 0.9375
n <- 5
nd <- 5
k <- 0
p_tie <- 0
factorial(n) /
(factorial(nd + k) * factorial(k) * factorial(n - nd - 2*k)) *
((1 - p_tie) / 2)^(nd + 2*k) *
p_tie^(n - nd - 2*k)
choose(n, nd + 2*k) * ifelse(k == 0, 1, prod((nd + k + 1):(nd + 2*k))) / factorial(k) *
((1 - p_tie) / 2)^(nd + 2*k) *
p_tie^(n - nd - 2*k)
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