Using Quarto

Introduction

Quarto is even fancier and possibly easier to use than R-markdown; it is run on RStudio, just like R-Markdown, and the coding is almost exactly the same, so that Rmd files can be compiled as qmd files with minor edits.

R-example

We simulate the amount of time it take for a head to appear, when tossing a bias coin.

flips <- function(p){
  x=0
  n=0
  while(x==0){
    x=rbinom(1,1,p)
    n=n+1
  }
n
}
sim = replicate(100000, flips(0.4))
mean(sim)

[1] 2.49501

1/0.4

[1] 2.5

Python-example

We do the same experiment in Python,

import numpy as np

def flips(p):
  x=0
  n=0
  while x==0:
    x=np.random.binomial(1,p,1)
    n=n+1
  return n

sim = [flips(0.4) for _ in range(100000)]
print(np.mean(sim))

2.49646

print(1/0.4)

2.5

Math

It appears that Quarto can easily handle Latex equation arrays without have the two dollar signs between the code, which allows for easier conversation into pdf.

Let \(U_1, U_2, \ldots\) be independent and uniformly distributed on the unit interval. By the law of large numbers and the change of variables formula, we have \[\begin{eqnarray*} \int_0 ^1 g(x) dx &=& \mathbb{E}g(U_1) \\ &=& \lim_{n \to \infty} \frac{1}{n} \sum_{i=1} ^n g(U_i) \end{eqnarray*}\]

Other notes

qmd Source

Version: 25 April 2023