Question

The statement rbinom(n,1, p) makes a sample of size n from a Bernoulli distribu- tion with success probability p. If you wanted to simulate n independent tosses of a fair coin with success probability p, you could use this command to do it. The successes would appear as 1s, and the failures as 0s. Suppose that you have a gambling game which pays off 2 when a coin is flipped and comes up heads and in which each toss costs 1 (regadless of whether you win or not) The coin is fair if the probability of getting a head is p0.5, but it could be unfair if p took on some other value. Write a function that simulates playing this game which starts with the player having 10 and runs until they become bankrupt (i.e. their total winnings become 0). The program should tel you when the bankruptcy happened (on which toss) and also plot out the path of winnings from 10 ui bankruptcy. Run the program and produce output for p- 0.5, p 17/35, and p 1/3.

Answer 1

RQUIRED R CODE:

x<-10
y<-c(10)
game<-function(p)
{
set.seed(20*p)
while(x>0)
{
z<-runif(1)
if(z<=p)
{
x<-x+1
y<-c(y,x)
}
else
{
x<-x-1
y<-c(y,x)
}
}
print(length(y)-1)
plot(y)
lines(y)
}
set.seed(100)
game(.5)
game(17/35)
game(1/3)

________________________________

OUTPUT FOR TOSS AT WHICH BANKRUPTCY HAPPEN IS

FOR P 0.5 IS 522

FOR P 17/35 IS 322

FOR P 1/3 IS 22

_________________________

PLOTS ARE

FOR P 0.5

FOR P 17/35 IS

FOR P 1/3 IS

____________________________________________

DON'T FORGET TO RATE THE ANSWER BY THUMBS UP TO SUPPORT MY WORK.

THANKS FOR ASKING THE PROBLEM .

CHEERS!

HAPPY CHEGGING!