Loop

For loop

Function

#Initial value
x=0
x[1]=35
a=37
m=16935
k=20

x[2]=(a*x[1])%%m
x[2]

## [1] 1295

x[3]=(a*x[2])%%m
x[3]

## [1] 14045

x[4]=(a*x[3]) %% m
x[4]

## [1] 11615

i 1 to k =20

i=1
x[i+1]=(a*x[i])%%m

for (i in 1:k) {
  x[i+1]=(a*x[i])%%m
}

print(x[-1])

##  [1]  1295 14045 11615  6380 15905 12695 12470  4145   950  1280 13490  8015
## [13]  8660 15590  1040  4610  1220 11270 10550   845

PsR=function(x,a,m,k)
{
  for (i in 1:k) {
    x[i+1]=(a*x[i])%%m
  }
  y=x/m
  return(y[-1])
}

PsR(35,37,16935,20)

##  [1] 0.07646885 0.82934751 0.68585769 0.37673457 0.93917921 0.74963094
##  [7] 0.73634485 0.24475937 0.05609684 0.07558311 0.79657514 0.47328019
## [13] 0.51136699 0.92057868 0.06141128 0.27221730 0.07204015 0.66548568
## [19] 0.62297018 0.04989666

Day II

For loop

Function

x=0

#Initial value

x[1]=53
a=137
m=1633933
k=100
for (i in 1:k) {
  x[i+1]=(a*x[i])%%m
}

print(x[-1])

##   [1]    7261  994757  665270 1275675 1570577 1123826  374460  649097  693907
##  [10]  297145 1494473  501176   35926   20063 1114698  757857  888630  831268
##  [19] 1142339 1276808   91865 1147974  414870 1283468 1004285  336673  374077
##  [28]  596626   41112  730545  414752 1267302  423476  828557  770932 1045972
##  [37] 1145993  143473   48605  123153  532631 1077395  549145   71947   53141
##  [46]  744585  704299   86916  469961  661270  727675   21562 1320061 1115727
##  [55]  898830  594735 1415978 1184892  570837 1409818  340972  963040 1221840
##  [64]  730914  465305   23398 1571593 1263018 1470501  484878 1070966 1302305
##  [73]  317088  958798  640686 1175533  922587  581578 1247402  965042 1496114
##  [82]  725993 1425061  795330 1120632 1570815 1156432 1573616 1540169  225796
##  [91] 1523258 1176855 1103701  885201  361495  506825  809839 1474432 1023425
## [100] 1324920

PsR=function(x,a,m,k)
{
  for (i in 1:k) {
    x[i+1]=(a*x[i])%%m
  }
  y=x/m
  return(y[-1])
}

PsR(53,137,16966635,100)->u

plot(u)

Example: 4a

p1 =0.20
p2 =0.15
p3 =0.25
p4 =0.40

PsR(x=40,a=137,m=16966635,k=1)->u

X={1,2,3,4}

ifelse(u<0.2,1,ifelse(u<0.35,2,ifelse(u<0.6,3,4)))

## [1] 1