# Soluz Lab 1 IS 2025

# Esercizio 1.
# a)
dbinom(3,size=5,prob=0.3)         # 0.1323

# b)
pbinom(3,size=10,prob=0.3)        # 0.6496

# c)
qbinom(0.95,size=100,prob=0.3)    # 38

# d)
sum(dbinom(3:5,size=10,prob=0.3))  # 0.5698682

# e)
rbinom(20,size=10,prob=0.3)


# Esercizio 2.
xx=seq(0,15,1)
yy=dpois(xx,3)
plot(xx,yy,type="h",lwd=2)
# per la binomiale
x=0:10
y=dbinom(0:10,10,0.3)
plot(x,y,type="p",pch=16,lwd=2)
plot(x,y,type="h",lwd=2)
title("")


# Esercizio 3.
# a)
curve(dnorm(x,-4,sqrt(1)),from=-10,to=12)
curve(dnorm(x,7,sqrt(1)), add=T, lty=2)

# b)
aa=rnorm(1000,0,1)
hist(aa,prob=T)
curve(dnorm(x,0,1), add=T)


# Esercizio 4.
curve(dexp(x,rate=1/0.5),from=0,to=5)
curve(dexp(x,rate=1),add=T,lty=2)
curve(dexp(x,rate=1/2),add=T,lty=3)


# Esercizio 5.
curve(dgamma(x,shape=1,scale=2),from=0,to=10)
curve(dgamma(x,shape=2,scale=2),add=T,lty=2)
curve(dgamma(x,shape=3,scale=2),add=T,lty=3)
curve(dgamma(x,shape=5,scale=1),add=T,lty=4)


# Esercizio 6.
curve(dnorm(x),from=-3,to=3)
pnorm(-1)


# Esercizio 7.
pnorm(3,1,sqrt(2))-pnorm(-2,1,sqrt(2))    # 0.904