Question

Suppose that your boss instead asks that you toss a fair coin six times, record the number of heads, and then repeat the process, for 2000 times in total. How might you simulate this process with a U(0,1) random number generator? Try to generate the outcome for each group of six tosses at once (i.e., use 2000 random numbers, rather than 12,000 individuals outcomes which you bundle into groups of size six).

Answer 1

Let, X denotes number of heads in 6 tosses of fair coin

We have to repeat this process 2000 times. We want such 2000 values of x using U(0,1) variable

First, select 2000 uniform(0,1) variates, let they are, y=(y1,y2, .................,y1999,y2000)

Now, treat them as the probabilities, now we will get values of binomail variable X(i) such that probability of X(i) is yi where X(i) is number of heads in 6 tosses of fair coin at i'th process

Here is the R code for same

y=runif(2000,0,1) # It gives 2000 random values between 0 and 1
X=qbinom(y,6,0.5) # It gives 2000 values of X, where X is defined above, here in binomail random variable, n=6, p = 0.5 and X is the assumed value whose probability is y