Pasha Zusmanovich - teachning

R code demonstrated at 6PAS2 Probability and Statistic 2, summer semester 2025/2026.

Class 2 (Feb 18 2026)

raw data (air pollution and temperature at Ostrava-Českobratrská during 24 hour period on Sep 20 2015)

pm25 <- c(5, 5, 7, 8, 9, 10, 8, 6, 6, 6, 6, 10, 11, 11, 13, 12, 12, 15, 14, 12, 11, 12, 14, 13) 
temp <- c(10, 10, 10, 10, 10, 10, 10, 8.5, 8.5, 8.5, 7, 6.5, 6.5, 7, 7, 7, 8, 6, 5.5, 5.5, 5.5, 4, 4, 5.5)

Displaying histogram of pm25:
1st way:

hhist <- function (v)
{
	u <- unique(sort(v));
	n <- length(u);
	d <- rep (0, times=length(u));
	for (i in (1:n))
	{
		for (val in v)
		{
			if (val == u[i])
			{
				d[i] <- d[i] + 1;
			}
		}
	}
	plot (u,d, lwd=10, type="h");
}

2nd way:

u <- unique(sort(pm25));
n <- length(u);
d <- rep (0, times=length(u));
for (i in (1:n))
{	
	d[i] = sum(pm25 == u[i]);
}	
plot (u,d, lwd=10, type="h")

3rd way: hist (pm25)

Plotting histogram of random normally distributed sample:
hist (rnorm (1000), 100)

Plot air pollution against temerature:

plot (temp, pm25)
abline (lm (pm25 ~ temp))

Plotting graph of a function:

x <- seq (-5,5,length=100)
plot (x, sin(x), type="l")

Normal distribution:

Norm <- function (x,sigma,m)
{
	return (1/(sigma * sqrt(2*pi)) * exp(-0.5*((x-m)/sigma)^2));
}

Plotting 3 normal distributions together:

plot (x, Norm(x,1,0), type="l")
lines (x, Norm(x,2,0), type="l", col="green")
lines (x, Norm(x,1,4), type="l", col="blue")

Load package MASS. Plotting histogram of SP500 data from there against normal distribution:

library (MASS)
hist (SP500, 100, freq=F)
lines (x, Norm(x, sd(SP500), mean(SP500)), type="l", col="blue")
lines (x, Norm(x, 0.8*sd(SP500), mean(SP500)), type="l", col="blue")

Laplace distribution:

Lap <- function (x,b,m)
{
	return (1/(2*b) * exp(- abs(x-m)/b));
}
lines (x, Lap(x, sd(SP500)/sqrt(2), mean(SP500)), type="l", col="green")

Logistic distribution:

Log <- function (x,s,m)
{
	f <- -(x-m)/s;
	e <- exp(f);
	return (e/(s*(1+e)^2));
}	
lines (x, Log(x, sd(SP500)*sqrt(3)/pi, mean(SP500)), type="l", col="red")

Created: Wed Sep 30 2015
Last modified: Wed Apr 1 2026 19:15:52 CEST