#Grzegorz Surdziel
path<-getwd()
factorial(9)
choose(9,8)
combn(4,3)
(omega <- 52^2)
sprzyja_A <- 4*52
sprzyja_B <- 4*52
(PA<-sprzyja_A/omega)* (PB <-sprzyja_B/omega )
(omega <- choose(52,2))
sprzyja_A <- choose(13,2)
sprzyja_B <- choose(16,2)
(PA <- sprzyja_A/omega)*(PB <- sprzyja_B/omega)
(PAB <- choose(4,2)/omega)
PX1=0.1;PX2=0.4;PX3=0.5
PApwX1=0.05; PApwX2=0.03; PApwX3=0.03
(PA <- PX1*PApwX1+PX2*PApwX2+PX3*PApwX3)
PX1 = 0.1; PX2 = 0.4 ; PX3 = 0.5
PApwX1 = 0.05 ; PApwX2 = 0.03 ; PApwX3 = 0.03
PA <- PX1*PApwX1+PX2*PApwX2+PX3*PApwX3
(PX3pwA <- (PX3*PApwX3)/PA)
dbinom(1, size=9, prob=0.02)
dbinom(2, size=10, prob=0.02)

PS = 0.98; PP = 0.02
(P = choose(9,1)*PS^8*PP^1)
(P = dbinom(1, size=9, prob=0.02))*PP

PS = 0.98; PP = 0.02
(P = choose(10,2)*PS^8*PP^2)
(P = dbinom(2, size=10, prob=0.02))

n = 410;q=0.01; lambda = q*n
(dpois(6, lambda=q*n))

(lambda^6*exp(-lambda)/factorial(6))

lambda <- 3
(dpois(3, lambda=3))

min = 2 ; max = 14; czas = 6

(p <- punif(czas,min = 2,max = 14,lower.tail = T))


(1-p)

pnorm(84, mean=96, sd=6, lower.tail=FALSE)
pnorm(-2,mean=0,sd=1,lower.tail=FALSE)
pnorm(2,mean=0,sd=1)

lambda = 3 ; czas = 3
pexp(czas, rate=1/lambda, lower.tail=FALSE)

exp(-1)