BTBsung, R - rextester

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#R version 3.3.2 
  
#Bai 0.1.1

tinhKyVong <- function(ds, n){
    i <- 0
    s <- 0
    for(i in 1:n){
        s <- s + ds[i]
    }
    s / n
}

tinhPhuongSai <- function(ds, n){
    i = 0
    s = 0
    tb = tinhKyVong(ds, n)
    for(i in 1:n){
        s = s + (ds[i] - tb)^2
    }
    s / (n - 1)
}

ds <- sample(1:10, size = 40, replace = TRUE)
tinhKyVong(ds, 40)
tinhPhuongSai(ds, 40)

#Bai 0.1.2
#a)

sixes <- function(n){
    for(i in 1:n){
        kq = sample(1:6,1)
        if(kq==6) return(TRUE)
    }
    return(FALSE)
}

sixes(20)

#b)
play <- function(n,N){
    count <- 0
    for(i in 1:N){
        if(sixes(n) == TRUE) count = count + 1
    }
    return(count/N)
}
    
play(5,20)
    
#Bai 0.1.5
    
X <- c(1.3975068, 1.1253621, 0.7472591, 0.8144085,1.8202663, 
      0.8671346, 1.4210106, 1.678400513697046, 0.6182268,
     1.9064036, 0.9360782, 1.1175578, 1.2527916, 1.9584229,
     1.3689436, 1.5685716, 1.0691046, 1.6625395, 1.7949509)

as.double(X)
u <- sum(X)/20
o2 <- sum((X-u)^2)/(20-1)
u
o2
    
#Bai 0.1.6
#a)
tungDongXuCanDoi <- function(n){
    gieo <- c("sap", "ngua")
    for(i in 1:n){
        kq <- sample(gieo)
        if(kq=="sap") print(1)
        if(kq=="ngua") print(0)
    }
}

tungDongXuCanDoi(10)
    
#b)
raSap <- function(){
    xs <- sample(1:100,1)
    if(xs >= 1 && xs <= 35) return(TRUE)
    return(FALSE)    
}
    
nhanTien <- function(n){
    tien <- 0
    for(i in 1:n){
        if(raSap()==TRUE) tien = tien + 10
        if(raSap()==FALSE) tien = tien - 10
    }
    return(tien)
}
        
nhanTien(10)

#Bai 0.2.1
        
x <- sample(1:100, size = 80, replace = TRUE)
x
timMucPhanVi <- function(x, p){
    if(p<0 || p>100) return(FALSE)
    sort(x, decreasing = FALSE)
    
    i <- (p/100)*length(x)

if(is.integer(i)== FALSE){
        round(i)
        return(x[i])
        }
    else{
        return(x[i]+(p/100)*(x[i+1]-x[i]))
    }
}
timMucPhanVi(x,25)
    
#Bai 0.2.2
    
#a)
height <- seq(130,190,1)
plot(height, dnorm(height, 156, 4.6),
     type= "l",
     ylab= "f(height)",
     xlab= "Height",
     main= "Ham mat do cua phu nu Viet Nam")
#b)
dnorm(160,156,4.6)

#c)
plot(height, pnorm(height, 156, 4.6),
     type= "l",
     ylab= "f(height)",
     xlab= "Height",
     main= "Ham phan phoi tich luy cua phu nu Viet Nam")    
#d)
pnorm(150,156,4.6)
    
#0.2.3 lam tuong tu 0.2.2
    
#0.2.4
#a) 
P <- function(k, lamda){#Ham tinh xac suat P(X<=k)
    s <- 0
    for(i in 0:k){
        s <- s + (lamda^i) * exp(-lamda) / factorial(i)
    }
    return (s)
}

P(2,4)
#b)
people <- seq(1,20,1)
plot(people,dpois(people,4),
     type= "l",
     ylab= "f(people)",
     xlab= "People",
     main= "Ham phan phoi tich luy cua khach hang doi giao dich ATM") 
#c)
#Do P(20,4)=1
X<-0:20
timMucPhanVi(X,75)
    
#0.2.5
#a)
tinhMatDoXacSuat <- function(x){
    a <- 2
    b <- 5
    f <- (b^a)/(P(a,4))*(x^(-a-1))*exp(-b/x)
    return (f)
}
tinhMatDoXacSuat(4)#x=4, anpha =2, beta = 5
x <- seq(1,10,0.5)
#b)
plot(x, tinhMatDoXacSuat(x),
     type= "l",
     ylab= "f(x)",
     xlab= "x",
     main= "Ham mat do xac suat cua X") 
f = function(x, a = 2, b = 5){(b^a)/(P(a,4))*(x^(-a-1))*exp(-b/x)}
#c)
integrate(function(x = 2.75) f(x,2,5) , lower = 0, upper = Inf)
    
#0.2.6
#a)
hamMatDo <- function(x){ return( 2 * exp(-2*x) ) }
x <- seq(1,20,1)
plot(x,hamMatDo(x),
     type = "l",
     xlab= "x",
     ylab= "f(x)",
     main= "Ham mat do cua A")
hamPhanPhoiTichLuy <- function(n){#P(X<=x)
   f<- function(x) 2 * exp(-2*x)
   s <- integrate(f,lower = 0, upper = n)
   return(s)
}

#c)
hamPhanPhoiTichLuy(5)

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