R

setwd("C:\\Users\\Linas\\Desktop\\R ND")
v = 5
n = 9
p = n/(v+n)

#1 uzduotis
#1.

x = 0:n
x
S = dbinom(x,n,p)    #randamos visos tikimybes
S
rbind(x,S)           #padaromas atsitiktinio dydzio skirstinys

#2. Pasiskirstymo funkcija

P = pbinom(x, n, p)
P

#3. Breziniai
png("Pirma.png")
par(mfrow=c(1,2))
plot(x,S, type="o", main="skirstinio daugiakampio brezinys")
plot(x,P, type="l", main="pasiskirstymo funkcijos brezinys")
dev.off()

#4. Vidutine

EX=sum(x*S)
EX
#EX = 5.785714, todel didziausia tikimybe yra pataikyti 6 baudas.

#5. P(S<5)

Tik = 1-dbinom(9, n, p)-dbinom(8, n, p)-dbinom(7, n, p)-dbinom(6, n, p)-dbinom(5, n, p)
Tik

#2 uzduotis
vid = v
stdn = n/10
F = function(x) dnorm(x,vid,stdn)
P2 = integrate(F, v-1, v+2)   #tikimybe, kad X igis reiksme intervale [v-1; v+2]
P2
png("Antras_brezinys.png")
curve(F, v-3, v+3)
x = seq(3, 20, by=0.1)
a = x[x>v-1 & x<v+2]
b = dnorm(a, vid, stdn)
polygon(c(v-1, a, v+2), c(0, b, 0), col="blue")
dev.off()

#3 uzduotis

R = n * 50

#1.

B = v * 2
D = rbinom(R, B, p)
D
png("trecias_brezinys.png")
table(D)/b
plot(table(D), type="h", freq=FALSE)
dev.off()

#2.

u = v
u
l = abs(n-v)
l
G = rnorm(R, u, l)
G
jpeg("ketvirtas_brezinys.jpeg")
hist(G, freq=FALSE)
x = seq(-21, 21, 0.1)
y = dnorm(x, u, l)
lines(x, y, col="green")
dev.off()

#4 uzduotis

K = read.csv("inflation.csv")
str(K)
data = K$dateid01
data
france = K$france
france
germany = K$germany
germany
x = 1990:2015
png("penktas_brezinys.png")
par(mfrow=c(1,2))
hist(france)
hist(germany)
dev.off()


png("sestas.png")
par(mfrow=c(1,2))
boxplot(france)
boxplot(germany)
dev.off()


mean(france)
var(france)
median(france)
sd(france)
min(france)
max(france)


mean(germany)
var(germany)
median(germany)
sd(germany)
min(germany)
max(germany)