#Random variables- generating, distribution functions

#0. random number seed; fix for reproducible simulations
  i <- 5
  set.seed(i)         #i must be between 0 and 1000

  # the same effect can be created by saving .Random.seed and then
  # assigning that value to .Random.seed later.

#1. random sampling
   z <- c(18,22,15,25,36)

   sample(x=z,size=3,replace=F)  #take a SRS w/o replacement from z
   sample(x=z,size=3,replace=T)  #now w/ replacement; as for bootstrap
   sample(x=z,size=3,replace=T,prob=c(0.1, 0.3, 0.2, 0.1, 0.3)) #unequal prob sampling

#2. univariate random variable generation (see p. 164, Table 5.1)
  #beta, binomial, Cauchy, normal, lognormal, gamma, F, poisson, Chi-square

  rbeta(n=10,shape1=3,shape2=4)    # ten obs'ns from Beta(3,4)
  rbinom(n=10,size=100,prob=0.2)   # ten obs'ns from Binomial(100,0.2)
  rnorm(n=10,mean=20,sd=5.1)       # ten obs'ns from Normal(20,5.1^2)
  rpois(n=30,lambda=3)             # ten obs'ns from Poisson(3) 
  
#3. percentages- for P-values in particular; can discard tables in back of stat texts...
  pnorm(q=1.645,mean=0,sd=1)
  1-pf(q=5.7,df1=3,df2=15)

#4. quantiles- for test statistics, for example
  qt(p=0.975,df=21)


#5. density function value; or probability for discrete valued rv
  dnorm(x=0.5,mean=0,sd=1)
  dpois(x=1,lambda=2)