x <- rpois(8,50) #Markov mean(x) * 9 #Chebychev mean(x) + 3 * sqrt(mean(x^2) - (mean(x))^2) my_fun <- function(t) {1/t*log(9/8 * sum(exp(t*x)))} optim(par = 1, fn = my_fun, lower = 1, upper = 100, method = "Brent") my_fun(1) optim(par = 1, fn = my_fun, lower = .1, upper = 15, method = "Brent")

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