Consider the game in which two players, Jan and Jim, take turns in tossing a fai
ID: 3069060 • Letter: C
Question
Consider the game in which two players, Jan and Jim, take turns in tossing a fair co If the outcome is heads, Jim gets $10 from Jan. Otherwise, Jan gets $10 from Jim. *(a) How is the game simulated as a Monte Carlo experiment? (b) Run the experiment for 5 replications of 10 tosses each. Use the first five columns 19-4. of the 0-1 random numbers in Table 19.1, with each column corresponding to one replication (c) Establish a 95% confidence interval on Jan's winnings. Cmprhe coni inc n eeetial i inningsExplanation / Answer
from the given problem p(H) =.5 and P(T)= 0.5
A) Then by monto carlo simulation method probability function , cumulative probability function and random number interval for the given experiment are given below
B) simulation of the experiment for 5 replications of 10 tosses each is given in the following table
form the above simulation in the 50 outcomes no of heads = 23
no.of tails= 27
Proportion of jan"s win= 27/50= 0.54=p
Expected jan"s winnings= np=50x0.54=27
standard deviation of jan;s winnings=sqrt of (npq)= sqrt of (50x0.54x0.46)=3.5242
c) 95% confidence interval for jan"s winnings
[27-1.96x0.4984 <= mean ,<= 27+1.96x0.4984] where 0.4984= standard error of mean
[26.02 <=mean<=27.98]
955 confidence limits for jan expected winning are [26.02 , 27.98]
D) Jan's expected theoratical winning is E(X)= nP=50x0.5= 25
but 95% confidence interval for jan;s expected earning is [26.02 ,27.98]
out come X P(X( cumulative probability Random number interval H 0.5 0.5 0.0 - 0.50 T 0.5 1.0 0.51 - 1.0