Simulation allows us to perform experiments without actually having to do the experiments in real li

1

• Simulation allows us to perform experiments
  without actually having to do the experiments in
  real life...this is done through the use of
  random numbers either generated from a random
  number table or from a computer program (such as
  R).
• random number tables have many thousands of
  digits (0-9) all occurring in approximately equal
  numbers in the table thus when choosing a digit
  at random it can be done with the uniform
  distribution (Prob(any one digit is chosen).1 )
  Then these digits can be used to simulate other
  distributions like the Bernoulli, binomial, etc.
• try some examples
• simulate the toss of a fair coin once 5 times
  etc.
• simulate a B(5,.5) r.v. (see the bottom of p.139
  for a better way)
• one son policy in a country can we simulate
  it to answer what would be the average number
  of children in a family? what would be the ratio
  of births of girls to births of boys?
• show the same methods in R using the r
  functions...

2

• HW Read section and try 4.77 and 4.78. Notice
  that 4.77 asks you to simulate 120 rolls of a
  balanced die. Using the random number table is a
  possibility, but lets try R also... try the
  following code
• the sample function allows you to randomly
  sample from
• a set of numbers with equal probability assigned
  to each
• number. thus in the line below we get a sample
  of 100
• of the digits 1-6, replaceT making sure of
  equal probs.
• xlt-sample(c(1,2,3,4,5,6),100, replaceT)
• table(x)
• the table function gives a frequency
  distribution of the
• vector x in this case shows how many 1s, 2s,
  etc.
• were randomly selected. to handle the example on
  p.140
• create a vector of probs to go with the vector
  of values
• prvectlt-c(.082,.205,.256,.214,.134,.067,.028,.01,.
  003,.001)
• ylt-c(09)
• xlt-sample(y,size100,replaceT,probprvect)