R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

X<-numeric (100)
X[1]<-2 #condición inicial
for (t in 2:100)  X[t]<-0.5*X[t-1]
X2<-X[35:60]
X2<-ts(X2,start=50)
plot(X2,type='l')

1B

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-((-1/4)*(X[t-1])+3)
X
##   [1] 1.000000 2.750000 2.312500 2.421875 2.394531 2.401367 2.399658 2.400085
##   [9] 2.399979 2.400005 2.399999 2.400000 2.400000 2.400000 2.400000 2.400000
##  [17] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [25] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [33] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [41] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [49] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [57] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [65] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [73] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [81] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [89] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [97] 2.400000 2.400000 2.400000 2.400000
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

1C

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-(-1/4)*(X[t-1])+3
X
##   [1] 1.000000 2.750000 2.312500 2.421875 2.394531 2.401367 2.399658 2.400085
##   [9] 2.399979 2.400005 2.399999 2.400000 2.400000 2.400000 2.400000 2.400000
##  [17] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [25] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [33] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [41] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [49] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [57] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [65] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [73] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [81] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [89] 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000 2.400000
##  [97] 2.400000 2.400000 2.400000 2.400000
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

1.2B

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-((68/5)*((-1/4)^(1))+(12/5))
X
##   [1]  1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
##  [26] -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
##  [51] -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
##  [76] -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

1.2c

X<-numeric(100)
X [1]<-1
for (t in 2:100)     
X[t]<-((68/5)*((-1/4)^(1))+(12/5))
X
##   [1]  1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
##  [26] -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
##  [51] -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
##  [76] -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

2B

X<-numeric(100)
X [1]<-2
X [2]<-4
for (t in 3:100)     
X[t]<-((-1/6)*(X[t-1])+(1/6)*(X[t-2]))
X
##   [1]  2.000000e+00  4.000000e+00 -3.333333e-01  7.222222e-01 -1.759259e-01
##   [6]  1.496914e-01 -5.426955e-02  3.399348e-02 -1.471051e-02  8.117332e-03
##  [11] -3.804639e-03  1.986995e-03 -9.652724e-04  4.920446e-04 -2.428862e-04
##  [16]  1.224885e-04 -6.089577e-05  3.056404e-05 -1.524330e-05  7.634557e-06
##  [21] -3.812976e-06  1.907922e-06 -9.534831e-07  4.769009e-07 -2.383973e-07
##  [26]  1.192164e-07 -5.960228e-08  2.980311e-08 -1.490090e-08  7.450668e-09
##  [31] -3.725261e-09  1.862655e-09 -9.313193e-10  4.656624e-10 -2.328303e-10
##  [36]  1.164154e-10 -5.820762e-11  2.910384e-11 -1.455191e-11  7.275959e-12
##  [41] -3.637978e-12  1.818990e-12 -9.094946e-13  4.547474e-13 -2.273737e-13
##  [46]  1.136868e-13 -5.684342e-14  2.842171e-14 -1.421085e-14  7.105427e-15
##  [51] -3.552714e-15  1.776357e-15 -8.881784e-16  4.440892e-16 -2.220446e-16
##  [56]  1.110223e-16 -5.551115e-17  2.775558e-17 -1.387779e-17  6.938894e-18
##  [61] -3.469447e-18  1.734723e-18 -8.673617e-19  4.336809e-19 -2.168404e-19
##  [66]  1.084202e-19 -5.421011e-20  2.710505e-20 -1.355253e-20  6.776264e-21
##  [71] -3.388132e-21  1.694066e-21 -8.470329e-22  4.235165e-22 -2.117582e-22
##  [76]  1.058791e-22 -5.293956e-23  2.646978e-23 -1.323489e-23  6.617445e-24
##  [81] -3.308722e-24  1.654361e-24 -8.271806e-25  4.135903e-25 -2.067952e-25
##  [86]  1.033976e-25 -5.169879e-26  2.584939e-26 -1.292470e-26  6.462349e-27
##  [91] -3.231174e-27  1.615587e-27 -8.077936e-28  4.038968e-28 -2.019484e-28
##  [96]  1.009742e-28 -5.048710e-29  2.524355e-29 -1.262177e-29  6.310887e-30
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

2.1B

X<-numeric(100)
X [1]<-2
X [2]<-4
for (t in 3:100)     
X[t]<-((-1/3)*(-1/6))+((2/3)*(1/6))
X
##   [1] 2.0000000 4.0000000 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##   [8] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [15] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [22] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [29] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [36] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [43] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [50] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [57] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [64] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [71] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [78] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [85] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [92] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [99] 0.1666667 0.1666667
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

2C

X<-numeric(100)
X [1]<-2
X [2]<-4
for (t in 3:100)     
X[t]<-((-1/6)*(X[t-1])+(1/6)*(X[t-2]))
X
##   [1]  2.000000e+00  4.000000e+00 -3.333333e-01  7.222222e-01 -1.759259e-01
##   [6]  1.496914e-01 -5.426955e-02  3.399348e-02 -1.471051e-02  8.117332e-03
##  [11] -3.804639e-03  1.986995e-03 -9.652724e-04  4.920446e-04 -2.428862e-04
##  [16]  1.224885e-04 -6.089577e-05  3.056404e-05 -1.524330e-05  7.634557e-06
##  [21] -3.812976e-06  1.907922e-06 -9.534831e-07  4.769009e-07 -2.383973e-07
##  [26]  1.192164e-07 -5.960228e-08  2.980311e-08 -1.490090e-08  7.450668e-09
##  [31] -3.725261e-09  1.862655e-09 -9.313193e-10  4.656624e-10 -2.328303e-10
##  [36]  1.164154e-10 -5.820762e-11  2.910384e-11 -1.455191e-11  7.275959e-12
##  [41] -3.637978e-12  1.818990e-12 -9.094946e-13  4.547474e-13 -2.273737e-13
##  [46]  1.136868e-13 -5.684342e-14  2.842171e-14 -1.421085e-14  7.105427e-15
##  [51] -3.552714e-15  1.776357e-15 -8.881784e-16  4.440892e-16 -2.220446e-16
##  [56]  1.110223e-16 -5.551115e-17  2.775558e-17 -1.387779e-17  6.938894e-18
##  [61] -3.469447e-18  1.734723e-18 -8.673617e-19  4.336809e-19 -2.168404e-19
##  [66]  1.084202e-19 -5.421011e-20  2.710505e-20 -1.355253e-20  6.776264e-21
##  [71] -3.388132e-21  1.694066e-21 -8.470329e-22  4.235165e-22 -2.117582e-22
##  [76]  1.058791e-22 -5.293956e-23  2.646978e-23 -1.323489e-23  6.617445e-24
##  [81] -3.308722e-24  1.654361e-24 -8.271806e-25  4.135903e-25 -2.067952e-25
##  [86]  1.033976e-25 -5.169879e-26  2.584939e-26 -1.292470e-26  6.462349e-27
##  [91] -3.231174e-27  1.615587e-27 -8.077936e-28  4.038968e-28 -2.019484e-28
##  [96]  1.009742e-28 -5.048710e-29  2.524355e-29 -1.262177e-29  6.310887e-30
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

2.2c

X<-numeric(100)
X [1]<-2
X [2]<-4
for (t in 3:100)     
X[t]<-((-1/3)*(-1/6))+((2/3)*(1/6))
X
##   [1] 2.0000000 4.0000000 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##   [8] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [15] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [22] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [29] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [36] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [43] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [50] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [57] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [64] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [71] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [78] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [85] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [92] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
##  [99] 0.1666667 0.1666667
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

3B

X<-numeric(100)
X [1]<-(-2/3)
X [2]<-(1/3)
for (t in 3:100)     
X[t]<-((-2/3)*(X[t-1])-(-1/9)*(X[t-2]))
X
##   [1] -6.666667e-01  3.333333e-01 -2.962963e-01  2.345679e-01 -1.893004e-01
##   [6]  1.522634e-01 -1.225423e-01  9.861302e-02 -7.935782e-02  6.386222e-02
##  [11] -5.139235e-02  4.135737e-02 -3.328184e-02  2.678315e-02 -2.155342e-02
##  [16]  1.734485e-02 -1.395806e-02  1.123258e-02 -9.039281e-03  7.274252e-03
##  [21] -5.853866e-03  4.710827e-03 -3.790981e-03  3.050746e-03 -2.455051e-03
##  [26]  1.975672e-03 -1.589898e-03  1.279451e-03 -1.029623e-03  8.285765e-04
##  [31] -6.667869e-04  5.365887e-04 -4.318132e-04  3.474964e-04 -2.796435e-04
##  [36]  2.250397e-04 -1.810980e-04  1.457364e-04 -1.172796e-04  9.437934e-05
##  [41] -7.595063e-05  6.112034e-05 -4.918585e-05  3.958172e-05 -3.185291e-05
##  [46]  2.563324e-05 -2.062804e-05  1.660016e-05 -1.335878e-05  1.075032e-05
##  [51] -8.651186e-06  6.961937e-06 -5.602534e-06  4.508571e-06 -3.628218e-06
##  [56]  2.919764e-06 -2.349645e-06  1.890848e-06 -1.521637e-06  1.224519e-06
##  [61] -9.854168e-07  7.930022e-07 -6.381589e-07  5.135506e-07 -4.132736e-07
##  [66]  3.325769e-07 -2.676372e-07  2.153778e-07 -1.733227e-07  1.394793e-07
##  [71] -1.122443e-07  9.032723e-08 -7.268974e-08  5.849619e-08 -4.707410e-08
##  [76]  3.788231e-08 -3.048533e-08  2.453270e-08 -1.974239e-08  1.588745e-08
##  [81] -1.278523e-08  1.028876e-08 -8.279754e-09  6.663032e-09 -5.361994e-09
##  [86]  4.314999e-09 -3.472443e-09  2.794407e-09 -2.248765e-09  1.809666e-09
##  [91] -1.456307e-09  1.171945e-09 -9.431087e-10  7.589553e-10 -6.107600e-10
##  [96]  4.915017e-10 -3.955300e-10  3.182980e-10 -2.561464e-10  2.061307e-10
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

3.1B

X<-numeric(100)
X [1]<-(-2/3)
X [2]<-(1/3)
for (t in 3:100)     
X[t]<-((1)*(-2/3))-((-3)*(-1/9))
X
##   [1] -0.6666667  0.3333333 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##   [7] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [13] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [19] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [25] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [31] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [37] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [43] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [49] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [55] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [61] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [67] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [73] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [79] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [85] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [91] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [97] -1.0000000 -1.0000000 -1.0000000 -1.0000000
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

3C

X<-numeric(100)
X [1]<-(-2/3)
X [2]<-(1/3)
for (t in 3:100)     
X[t]<-((-2/3)*(X[t-1])-(-1/9)*(X[t-2]))
X
##   [1] -6.666667e-01  3.333333e-01 -2.962963e-01  2.345679e-01 -1.893004e-01
##   [6]  1.522634e-01 -1.225423e-01  9.861302e-02 -7.935782e-02  6.386222e-02
##  [11] -5.139235e-02  4.135737e-02 -3.328184e-02  2.678315e-02 -2.155342e-02
##  [16]  1.734485e-02 -1.395806e-02  1.123258e-02 -9.039281e-03  7.274252e-03
##  [21] -5.853866e-03  4.710827e-03 -3.790981e-03  3.050746e-03 -2.455051e-03
##  [26]  1.975672e-03 -1.589898e-03  1.279451e-03 -1.029623e-03  8.285765e-04
##  [31] -6.667869e-04  5.365887e-04 -4.318132e-04  3.474964e-04 -2.796435e-04
##  [36]  2.250397e-04 -1.810980e-04  1.457364e-04 -1.172796e-04  9.437934e-05
##  [41] -7.595063e-05  6.112034e-05 -4.918585e-05  3.958172e-05 -3.185291e-05
##  [46]  2.563324e-05 -2.062804e-05  1.660016e-05 -1.335878e-05  1.075032e-05
##  [51] -8.651186e-06  6.961937e-06 -5.602534e-06  4.508571e-06 -3.628218e-06
##  [56]  2.919764e-06 -2.349645e-06  1.890848e-06 -1.521637e-06  1.224519e-06
##  [61] -9.854168e-07  7.930022e-07 -6.381589e-07  5.135506e-07 -4.132736e-07
##  [66]  3.325769e-07 -2.676372e-07  2.153778e-07 -1.733227e-07  1.394793e-07
##  [71] -1.122443e-07  9.032723e-08 -7.268974e-08  5.849619e-08 -4.707410e-08
##  [76]  3.788231e-08 -3.048533e-08  2.453270e-08 -1.974239e-08  1.588745e-08
##  [81] -1.278523e-08  1.028876e-08 -8.279754e-09  6.663032e-09 -5.361994e-09
##  [86]  4.314999e-09 -3.472443e-09  2.794407e-09 -2.248765e-09  1.809666e-09
##  [91] -1.456307e-09  1.171945e-09 -9.431087e-10  7.589553e-10 -6.107600e-10
##  [96]  4.915017e-10 -3.955300e-10  3.182980e-10 -2.561464e-10  2.061307e-10
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

3.2C

X<-numeric(100)
X [1]<-(-2/3)
X [2]<-(1/3)
for (t in 3:100)     
X[t]<-((1)*(-2/3))-((-3)*(-1/9))
X
##   [1] -0.6666667  0.3333333 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##   [7] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [13] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [19] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [25] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [31] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [37] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [43] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [49] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [55] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [61] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [67] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [73] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [79] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [85] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [91] -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000 -1.0000000
##  [97] -1.0000000 -1.0000000 -1.0000000 -1.0000000
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

4b

X<-numeric(100)
X [1]<-(1)
X [2]<-(4)
for (t in 3:100)     
X[t]<-((-5/3)*(X[t-1])+(2/3)*(X[t-2]))
X
##   [1]  1.000000e+00  4.000000e+00 -6.000000e+00  1.266667e+01 -2.511111e+01
##   [6]  5.029630e+01 -1.005679e+02  2.011440e+02 -4.022853e+02  8.045716e+02
##  [11] -1.609143e+03  3.218286e+03 -6.436571e+03  1.287314e+04 -2.574629e+04
##  [16]  5.149257e+04 -1.029851e+05  2.059703e+05 -4.119406e+05  8.238811e+05
##  [21] -1.647762e+06  3.295525e+06 -6.591049e+06  1.318210e+07 -2.636420e+07
##  [26]  5.272839e+07 -1.054568e+08  2.109136e+08 -4.218271e+08  8.436543e+08
##  [31] -1.687309e+09  3.374617e+09 -6.749234e+09  1.349847e+10 -2.699694e+10
##  [36]  5.399387e+10 -1.079877e+11  2.159755e+11 -4.319510e+11  8.639020e+11
##  [41] -1.727804e+12  3.455608e+12 -6.911216e+12  1.382243e+13 -2.764486e+13
##  [46]  5.528973e+13 -1.105795e+14  2.211589e+14 -4.423178e+14  8.846356e+14
##  [51] -1.769271e+15  3.538543e+15 -7.077085e+15  1.415417e+16 -2.830834e+16
##  [56]  5.661668e+16 -1.132334e+17  2.264667e+17 -4.529334e+17  9.058669e+17
##  [61] -1.811734e+18  3.623468e+18 -7.246935e+18  1.449387e+19 -2.898774e+19
##  [66]  5.797548e+19 -1.159510e+20  2.319019e+20 -4.638039e+20  9.276077e+20
##  [71] -1.855215e+21  3.710431e+21 -7.420862e+21  1.484172e+22 -2.968345e+22
##  [76]  5.936689e+22 -1.187338e+23  2.374676e+23 -4.749351e+23  9.498703e+23
##  [81] -1.899741e+24  3.799481e+24 -7.598962e+24  1.519792e+25 -3.039585e+25
##  [86]  6.079170e+25 -1.215834e+26  2.431668e+26 -4.863336e+26  9.726672e+26
##  [91] -1.945334e+27  3.890669e+27 -7.781337e+27  1.556267e+28 -3.112535e+28
##  [96]  6.225070e+28 -1.245014e+29  2.490028e+29 -4.980056e+29  9.960112e+29
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

4.2B

X<-numeric(100)
X [1]<-(1)
X [2]<-(4)
for (t in 3:100)     
X[t]<-((9/-15)*(-5/3))+((6)*(2/3))
X
##   [1] 1 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
##  [38] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
##  [75] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

4c

X<-numeric(100)
X [1]<-(1)
X [2]<-(4)
for (t in 3:100)     
X[t]<-((-5/3)*(X[t-1])+(2/3)*(X[t-2]))
X
##   [1]  1.000000e+00  4.000000e+00 -6.000000e+00  1.266667e+01 -2.511111e+01
##   [6]  5.029630e+01 -1.005679e+02  2.011440e+02 -4.022853e+02  8.045716e+02
##  [11] -1.609143e+03  3.218286e+03 -6.436571e+03  1.287314e+04 -2.574629e+04
##  [16]  5.149257e+04 -1.029851e+05  2.059703e+05 -4.119406e+05  8.238811e+05
##  [21] -1.647762e+06  3.295525e+06 -6.591049e+06  1.318210e+07 -2.636420e+07
##  [26]  5.272839e+07 -1.054568e+08  2.109136e+08 -4.218271e+08  8.436543e+08
##  [31] -1.687309e+09  3.374617e+09 -6.749234e+09  1.349847e+10 -2.699694e+10
##  [36]  5.399387e+10 -1.079877e+11  2.159755e+11 -4.319510e+11  8.639020e+11
##  [41] -1.727804e+12  3.455608e+12 -6.911216e+12  1.382243e+13 -2.764486e+13
##  [46]  5.528973e+13 -1.105795e+14  2.211589e+14 -4.423178e+14  8.846356e+14
##  [51] -1.769271e+15  3.538543e+15 -7.077085e+15  1.415417e+16 -2.830834e+16
##  [56]  5.661668e+16 -1.132334e+17  2.264667e+17 -4.529334e+17  9.058669e+17
##  [61] -1.811734e+18  3.623468e+18 -7.246935e+18  1.449387e+19 -2.898774e+19
##  [66]  5.797548e+19 -1.159510e+20  2.319019e+20 -4.638039e+20  9.276077e+20
##  [71] -1.855215e+21  3.710431e+21 -7.420862e+21  1.484172e+22 -2.968345e+22
##  [76]  5.936689e+22 -1.187338e+23  2.374676e+23 -4.749351e+23  9.498703e+23
##  [81] -1.899741e+24  3.799481e+24 -7.598962e+24  1.519792e+25 -3.039585e+25
##  [86]  6.079170e+25 -1.215834e+26  2.431668e+26 -4.863336e+26  9.726672e+26
##  [91] -1.945334e+27  3.890669e+27 -7.781337e+27  1.556267e+28 -3.112535e+28
##  [96]  6.225070e+28 -1.245014e+29  2.490028e+29 -4.980056e+29  9.960112e+29
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

4.2C

X<-numeric(100)
X [1]<-(1)
X [2]<-(4)
for (t in 3:100)     
X[t]<-((9/-15)*(-5/3))+((6)*(2/3))
X
##   [1] 1 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
##  [38] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
##  [75] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

5b

X<-numeric(100)
X [1]<-(0)
X [2]<-(7)
for (t in 3:100)     
X[t]<-((1/2)*(X[t-1])+(1/4)*(X[t-2])+1)
X
##   [1] 0.000000 7.000000 4.500000 5.000000 4.625000 4.562500 4.437500 4.359375
##   [9] 4.289062 4.234375 4.189453 4.153320 4.124023 4.100342 4.081177 4.065674
##  [17] 4.053131 4.042984 4.034775 4.028133 4.022760 4.018414 4.014897 4.012052
##  [25] 4.009750 4.007888 4.006382 4.005163 4.004177 4.003379 4.002734 4.002212
##  [33] 4.001789 4.001448 4.001171 4.000947 4.000766 4.000620 4.000502 4.000406
##  [41] 4.000328 4.000266 4.000215 4.000174 4.000141 4.000114 4.000092 4.000074
##  [49] 4.000060 4.000049 4.000039 4.000032 4.000026 4.000021 4.000017 4.000014
##  [57] 4.000011 4.000009 4.000007 4.000006 4.000005 4.000004 4.000003 4.000003
##  [65] 4.000002 4.000002 4.000001 4.000001 4.000001 4.000001 4.000001 4.000000
##  [73] 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000
##  [81] 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000
##  [89] 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000
##  [97] 4.000000 4.000000 4.000000 4.000000
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

5.2B

X<-numeric(100)
X [1]<-(0)
X [2]<-(7)
for (t in 3:100)     
X[t]<-((0)*(-1/2))-((-28)*(-1/4)+4/5)
X
##   [1]  0.0  7.0 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [16] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [31] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [46] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [61] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [76] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [91] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
X1<-X[40:60]
X1<-ts(X1,start=0)
plot(X1,type='l')

5c

X<-numeric(100)
X [1]<-(0)
X [2]<-(7)
for (t in 3:100)     
X[t]<-((1/2)*(X[t-1])+(1/4)*(X[t-2])+1)
X
##   [1] 0.000000 7.000000 4.500000 5.000000 4.625000 4.562500 4.437500 4.359375
##   [9] 4.289062 4.234375 4.189453 4.153320 4.124023 4.100342 4.081177 4.065674
##  [17] 4.053131 4.042984 4.034775 4.028133 4.022760 4.018414 4.014897 4.012052
##  [25] 4.009750 4.007888 4.006382 4.005163 4.004177 4.003379 4.002734 4.002212
##  [33] 4.001789 4.001448 4.001171 4.000947 4.000766 4.000620 4.000502 4.000406
##  [41] 4.000328 4.000266 4.000215 4.000174 4.000141 4.000114 4.000092 4.000074
##  [49] 4.000060 4.000049 4.000039 4.000032 4.000026 4.000021 4.000017 4.000014
##  [57] 4.000011 4.000009 4.000007 4.000006 4.000005 4.000004 4.000003 4.000003
##  [65] 4.000002 4.000002 4.000001 4.000001 4.000001 4.000001 4.000001 4.000000
##  [73] 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000
##  [81] 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000
##  [89] 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000 4.000000
##  [97] 4.000000 4.000000 4.000000 4.000000
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')

5.2c

X<-numeric(100)
X [1]<-(0)
X [2]<-(7)
for (t in 3:100)     
X[t]<-((0)*(-1/2))-((-28)*(-1/4)+4/5)
X
##   [1]  0.0  7.0 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [16] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [31] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [46] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [61] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [76] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
##  [91] -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8 -7.8
X1<-X[80:100]
X1<-ts(X1,start=0)
plot(X1,type='l')