I need help with the following problem, specifically problem 2. I will have all the details of the exercise below. It is from the Quantitative Social Science book by Imai and uses R for statistical analysis. I figured out problem 1, but an stuck on problem 2.

"In this exercise, we use the rules of probability to detect election by examining voting patterns in the 2011 Russian state Duma election. The state Duma is the federal legislature of Russia. The ruling political party, United Russia, won this election, but to many accusations of election fraud, which the Kremlin, or Russian government, denied. Some protesters highlighted the irregular patterns of voting as evidence of election fraud. In particular, the protesters pointed out the relatively high frequency of common fractions such as 1/4, 1/3, and 1/2 in the official vote shares. We analyze the official election results ,contained in the Russia2011 data frame, In the R datafile Fraud.Rdata, to investigate whether there is any evidence for election fraud. The R datafile can be loaded using the load() function. The variables in the russia2011 data frame include N = the total number of voters in a precinct, turnout = total turnout in the precinct, and votes = total number of votes for the winner in a precinct."

"Problem 1: To analyze the 2011 Russian election results, first compute United Russia's vote share as a proportion of the voters who turned out. Identify the 10 most frequently occurring fractions for the vote share. You will make a histogram that sets the number of bins to the number of unique fractions, with one bar created for each uniquely observed fraction, to differentiate between similar fractions like 1/2 and 51/100. This can be done by using the breaks argument in the hist() function. What does this histogram look like with fractions with low numerators and denominators such as 1/2 and 1/3?"

R code:

load("fraud.RData")

vote.share = russia2011$votes/russia2011$turnout

vote.share.10 = sort(table(vote.share), decreasing = TRUE)[1:10]

unique.fra = unique(vote.share)

hist(vote.share, breaks = length(unique.fra), ylim = c(0, 400))

"Problem 2: The existence of high frequences at low fractions may not imply election fraud. Indeed, more numbers are divisible by smaller integers like 2, 3, and 4, than by larger integers like 22, 23, and 24. To investigate that the low fractions arose by chance, assume probability model. the turnout for a precinct has a binomial distribution, whose size equals the number of voters and success probability equals the turnout rate for the precinct. The vote share for United Russia in this precinct is assumed to follow a binomial distribution, conditional on the turnout, where the size equals the number of voters who turned out and the success probability equals the observed vote share in the precinct. Conduct a Monte Carlo simulation under this alternative assumption (1000 simulation should be sufficient). what are the 10 frequent vote share values? You will make a histogram similar to the one in the previous question. Briefly comment on the results you obtain."

Any help with the R code for this would help greatly. Thanks!