Code from class

# Write a function sd that computes the standard deviation of x “from scratch”. Include a parameter na.rm in it


#𝐿(𝜆;𝑥)=−𝑛𝜆+𝑙𝑜𝑔(𝜆)⋅∑𝑥𝑖
# is the log likelihood function of a Poisson variable x with parameter 𝜆>0

# Write a function loglikpois with parameters lambda and x (a vector) that computes the log likelihood value for lambda given observations x.

loglikpois <- function(lambda, x) {
  #𝐿(𝜆;𝑥)=−𝑛𝜆+𝑙𝑜𝑔(𝜆)⋅∑𝑥𝑖
  stopifnot(lambda >= 0, all(x >= 0))
  x_int <- as.integer(x)
  if (!all(x_int == x)) { # we need a better error message here
    stop("all values in x have to be integer values. ")
  }
  n <- length(x)

  -n*lambda + log(lambda)*sum(x)
}
# Make sure to check that lambda is positive; return an error message (using stop()) if it is not.
# Plot the likelihood values for lambda between 0 and 10 for x = c(1, 3, 2, 3, 0, 1, 0, 1, 3, 3)

x = c(1, 3, 2, 3, 0, 1, 0, 1, 3, 3.000, 4)
loglikpois(lambda = 1, x)
loglikpois(lambda = 1.5, x)

library(ggplot2)
ggplot() +
  geom_function(fun=loglikpois, args = list(x = x), xlim=c(0, 10))
mean(x)



#############

binom <- function(n, k) {
  stopifnot(n >= k, n >= 0, k >= 0)
  factorial(n)/(factorial(k)*factorial(n-k))
}

binom2 <- function(n, k) {
  stopifnot(n > k, n >= 0, k >= 0)
  # get factorial (n-k) out of the denominator
  k <- max(k, n-k)
  prod((k+1):n)/(factorial(n-k))
}


binom2(10, 5) == choose(10,5)

binom2(175,173)
binom2(175,2)

binom(175,2)
choose(175, 2)