1) x <- c(-2,-1,0,1,2)
	pnorm(x, sd=2)
	
2) x <- c(0,1,2,5,8,10,15,20)
	ppois(x,5)	
	pbinom(x, size=20, prob=0.25)

3) x <- seq(0, 55, by=1)
	p <- c(0.1, 0.4, 0.7)
	n=50
	plot(x, dbinom(x, size = n, prob = p[1]), type="l", main ="Binomial PMF",
			 ylab = "dbinom(x,n,p)")
	for(i in 2:3)
		lines(x, dbinom(x, size = n, prob = p[i]), col=i)
	legend(x="topright", legend=paste0("p= ", p), col=1:3, lty=1, cex=1.3)		

4) x <- seq(0, 55, by=1)
	p <- c(0.1, 0.4, 0.7)
	plot(x, dgeom(x, p[1]), type="l", ylim=c(0,0.75),
		 main ="Geometric PMF", ylab = "dgeom(x,p)")
	for(i in 2:3)
		lines(x, dgeom(x, p[i]), col=i)
	legend(x="topright", legend=paste0("p= ", p), col=1:3, lty=1, cex=1.3)

5) x <- seq(0, 55, by=1)
	lambda <- c(1, 5, 15, 25, 40)
	plot(x, dpois(x, lambda[1]), type="l", 
		 main ="Geometric PMF", ylab = expression(dpois(x,lambda)))
	for(i in 2:length(lambda))
		lines(x, dpois(x, lambda[i]), col=i)
	text <- paste0(expression(lambda), " ", lambda)
	vals<-paste0(" ", lambda)
	legend(x="topright", legend=text, 
			col=1:length(lambda), lty=1)
			
6)	x <- seq(-5, 5, length=500)
	nuval <- c(1, 2, 3, 5, 10)
	plot(x, dt(x, nuval[1]), type="l", 
		 main ="Student's t PMF", ylab = expression(dt(x,nu)), ylim=c(0,0.45))
	for(i in 2:length(nuval))
		lines(x, dt(x, nuval[i]), col=i)
	text <- paste0(expression(nu), " ", nuval)
	legend(x="topright", legend=text, 
			col=1:length(nuval), lty=1)	

7) (a)	pnorm(27.5,22,sd=5)-pnorm(16.2,22,sd=5)
	(b)   1-pnorm(29,22,sd=5)			
	(c)	pnorm(17,22,sd=5)
	(d)   pnorm(15,22,sd=5)+1-pnorm(25,22,sd=5)
	
8) (a)	sum(dbinom(c(20,25),50,prob=0.6))
	(b)	pbinom(19,50,prob=0.6)
	(c)	pbinom(31,50,prob=0.6)-pbinom(19,50,prob=0.6)	
	
9)	
	dunifD <- function(x, min=0, max=100) {
		if(x>=min & x<=max & round(x)==x) return(1/(max-min+1)) 
			else return(0)
	}		
	punifD <- function(q, min=0, max=100){ 
			if(q<min) return(0)
			else{ if(q>=max) return(1)
					else return((floor(q)-min+1)/(max-min+1))
			}		
	}	
	qunifD <- function(p, min=0, max=100){ 
		if(0<=p&& p<=1) return(floor(p*(max-min+1)))
		else stop	("p=", p, " deve essere in [0,1]")
	}
	runifD <- function(n, min=0, max=100){ return(sample(min:max, n, replace=T))}