num<-Rmpfr::mpfr(4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727   ,10000)
num_2<-Rmpfr::mpfr(7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274    ,10000)

count_num<-function(x){
  buf <- c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
  for(i in 0:99) {
    if(x %% 10==0) {
      buf[1] <- buf[1] + 1
    }
    if(x %% 10==1) {
      buf[2] <- buf[2] + 1
    }
    if(x %% 10==2) {
      buf[3] <- buf[3] + 1
    }
    if(x %% 10==3) {
      buf[4] <- buf[4] + 1
    }
    if(x %% 10==4) {
      buf[5] <- buf[5] + 1
    }
    if(x %% 10==5) {
      buf[6] <- buf[6] + 1
    }
    if(x %% 10==6) {
      buf[7] <- buf[7] + 1
    }
    if(x %% 10==7) {
      buf[8] <- buf[8] + 1
    }
    if(x %% 10==8) {
      buf[9] <- buf[9] + 1
    }
    if(x %% 10==9) {
      buf[10] <- buf[10] + 1
    }
    x <- x%/%10
  }
  return(buf)
}



count<-count_num(num)
count_2<-count_num(num_2)


matrice <- matrix(c(count[1],count[2],count[3],count[4],count[5],count[6],count[7],count[8],count[9],count[10],10,10,10,10,10,10,10,10,10,10), nrow = 2, byrow = TRUE)
matrice

text_h0<-chisq.test(matrice)
text_h0

if (text_h0[1] < 16.91898) {
  print('h0:цифры распеделяются равномерно при p=0.95')
}else {
  print('h0:цифры не распеделяются равномерно при p=0.95')
}

matrice <- matrix(c(count[1],count[2],count[3],count[4],count[5],count[6],count[7],count[8],count[9],count[10],5,7,10,13,15,15,13,10,7,5), nrow = 2, byrow = TRUE)
matrice
text_h1.1<-nortest::pearson.test(matrice)
text_h1.1
text_h1.2<-chisq.test(matrice)
text_h1.2

if (text_h1.2[1] < 3.32511) {
  print('h0:цифры распределяются по нормальному закону при p=0.95')
}else {
  print('h0:цифры не распределяются по нормальному закону при p=0.95')
}


matrice <- matrix(c(count[1],count[2],count[3],count[4],count[5],count[6],count[7],count[8],count[9],count[10],count_2[1],count_2[2],count_2[3],count_2[4],count_2[5],count_2[6],count_2[7],count_2[8],count_2[9],count_2[10]), nrow = 2, byrow = TRUE)
matrice
text2.1<-nortest::pearson.test(matrice)
text2.1
text2.2<-chisq.test(matrice)
text2.2

if (1.0684 > 0.95) {
  print('однородны при а=0.05')
}else {
  print('неоднородные при а=0.05')
}

matrice <- matrix(c(122,93,34,103,69,39,95,115,55), nrow = 3, byrow = TRUE)
matrice

ksi_2<-function(x) {
  ksi <- 0
  mat <- matrix(c(0,0,0,0,0,0,0,0,0), nrow = 3, byrow = TRUE)

  for (i in 0:2){
    for (j in 0:2){
      mat[i+1,j+1] <- x[i+1,j+1] * x[i+1,j+1]
      mat[i+1,j+1] <- mat[i+1,j+1]/((x[i+1,1]+x[i+1,2]+x[i+1,3])*(x[1,j+1]+x[2,j+1]+x[3,j+1]))
    }
  }

  for (l in 0:2){
    for (f in 0:2){
      ksi <- ksi + mat[l+1,f+1]
    }
  }

  ksi <- (ksi - 1) * 795

  return(ksi)
}

ksi_2(matrice)
if (ksi_2(matrice) < 9.48773){
  print('независимы при p=0.05')
}else {
  print('зависимы при p=0.05')
}