R: Matematika Dasar
Contoh operasi matematika
2 ^ 2
2 * 2
2 / 2
2 + 2
2 - 2
4 * 3 ^ 3
vector -4 s/d 3
-4:3
abs remainder
absolute
abs(-4:3)
remainder
(-4:3) %% 2
(-4:3) %/% 3
sign
sign(-4:3)
round
round(7/18,2)
7/118
options(digits=2) 7/118
floor(0.39)
ceiling(0.39)
summary functions
sum(1:3) prod(c(3,5,7)) min(c(1,6,-14,-154,0)) max(c(1,6,-14,-154,0)) range(c(1,6,-14,-154,0))
any(c(1,6,-14,-154,0)<0) which(c(1,6,-14,-154,0)<0) all(c(1,6,-14,-154,0)<0) # all checks if criteria is met by each element
Complex
# Plot of Characteristic Function of a U(-1,1) Random Variable a <- -1; b <- 1 t <- seq(-20,20,.1) chu <- (exp(1i*t*b)-exp(1i*t*a))/(1i*t*(b-a)) plot(t,chu,"l",ylab=(expression(varphi(t))),main="Characteristic Function of Uniform Distribution [-1, 1]")
# Plot of Characteristic Function of a N(0,1) Variable mu <- 0; sigma <- 1 t <- seq(-5,5,0.1) chsnv <- exp(1i*t*mu-.5*(sigma ̂ 2)*(t ̂ 2)) plot(t,chsnv,"l",ylab=(expression(varphi(t))),main="Characteristic Function of Standard Normal Distribution")
# Plot of Characteristic Function of Poisson Random Variable lambda <- 6 t <- seq(0,20,.1) chpois <- exp(lambda*(exp(1i*t)-1)) plot(t,chpois,"l") # Warning omitted and left as exercise # for the reader to interpret
Trigonometry
sin(pi/2)
tan(pi/4)
cos(pi)