[PA]Lab3

#I.1
normal_density = function (m,d){
  t=seq(-6,6,length=400)
  f=1/sqrt(2*d*pi)*exp(-(t-m)^2/(2*d^2))
  plot(t,f,type="l", lwd=1)
}

normal_density(0,4)
normal_density(2,5)
normal_density(1,9)

#I.2
normal_density2 = function (m,d){
  d=sqrt(d);
  t=seq(m-d,d+m,length=2*d)
  f=1/sqrt(2*d*pi)*exp(-(t-m)^2/(2*d^2))
  plot(t,f,type="l", lwd=1)
}
normal_density4 = function (m,d){
  d=sqrt(d);
  t=seq(m-2*d,2*d+m,length=4*d)
  f=1/sqrt(2*d*pi)*exp(-(t-m)^2/(2*d^2))
  plot(t,f,type="l", lwd=1)
}
normal_density6 = function (m,d){
  d=sqrt(d);
  t=seq(m-3*d,m+3*d,length=6*d)
  f=1/sqrt(2*d*pi)*exp(-(t-m)^2/(2*d^2))
  plot(t,f,type="l", lwd=1)
}

normal_density2(2,7)
normal_density2(3,5)

normal_density4(0,4)
normal_density4(10,9)

normal_density6(4,2)
normal_density6(3,5)

#I.3
normal_density = function (m,d){
  t=seq(-6,6,length=400)
  f=1/sqrt(2*d*pi)*exp(-(t-m)^2/(2*d^2))
  plot(t,f,type="l", lwd=1)
}

normal_density(0,3)
normal_density(5,9)
normal_density(1,8)




#II.1
selection_mean = function(filename){
  x=scan(filename);
  m=mean(x);
  print m;
}

#II.2
selection_mean("sample.txt")

#II.3
selection_mean2 = function(filename, d){
  x=scan(filename);
  m=mean(x);
  D=d/length(x);
  D=sqrt(D);
  print(m);
  print(D);
}

selection_mean2("sample.txt",2)


#III.1
zconfidence_interval = function(alfa, sigma, n, sample_mean){
  critical_z=qnorm(1-alfa/2,0,1);
  a=sample_mean - critical_z*sigma/sqrt(n);
  b=sample_mean + critical_z*sigma/sqrt(n);
  interval=c(a,b);
  print(interval);
}

#III.2
sigma=100;
n=25;
sample_mean=67.53;
alfa=0.1;
zconfidence_interval(alfa, sqrt(sigma), n,sample_mean);

#III.3
sigma=0.5;
n=50;
sample_mean=5;
alfa=0.05;
zconfidence_interval(alfa,sigma, n,sample_mean);

#III.4
sigma=140;
n=100;
sample_mean=1280;
alfa=0.01;
zconfidence_interval(alfa,sqrt(sigma), n,sample_mean);

#III.5
zconfidence_interval = function(alfa, sigma, n, sample_mean){
  critical_z=qnorm(1-alfa/2,0,1);
  a=sample_mean - critical_z*sigma/sqrt(n);
  b=sample_mean + critical_z*sigma/sqrt(n);
  interval=c(a,b);
  print(interval);
}


sigma=5;
n=35;
sample_mean=60;
alfa=0.1;
zconfidence_interval(alfa,sqrt(sigma), n,sample_mean);
alfa=0.05;
zconfidence_interval(alfa,sqrt(sigma), n,sample_mean);
alfa=0.01;
zconfidence_interval(alfa,sqrt(sigma), n,sample_mean);

#III.6
zconfidence_interval = function(filename, alfa, sigma){
  x=scan(filename);
  sample_mean=mean(x);
  critical_z=qnorm(1-alfa/2,0,1);
  a=sample_mean - critical_z*sigma/sqrt(n);
  b=sample_mean + critical_z*sigma/sqrt(n);
  interval=c(a,b);
  print(interval);
}

zconfidence_interval("sample.txt",0.05, 2)