[SOLVED] Fe515 assignment 2: more simulations

In the board game monopoly, a player tosses two dices together and the sum of the two dices
points is the number of steps he or she should go.For example a player gets a 2 and a 3, then
he or she should go 5 steps forward. If the two dices give the same number (for example two
2), which is called a “double”, after moving forward (4 steps), the player gets another chance to
toss and move forward again. However, if someone tosses 3 consecutive doubles, he or she will
be sent to jail.Consider that you are tossing two fair dices for many times. You won’t stop until you get 3
doubles. After you stop, take down the number of tosses you use. Use a loop to repeat this at
least 1000 times. Calculate the average of the 1000 results, that is, how many tosses is needed
on average, to be able to get three consecutive doubles.The function hist() can be used to plot a histogram of frequency (by default) or a histogram
of density (by setting the argument freq to be FALSE).1. Fit normal density
• Generate 1000 standard normal random numbers and save them to x.
• Use hist() to draw its density.
• Create a vector xfit using seq() function. Use the following values for the arguments
of seq(): from=min(x), to = max(x) and by=0.1.• Run lines(xfit,dnorm(xfit,mean=0,sd=1)).
• You should see that the theoretical density curve is roughly going through the edge of
the data density histogram. Try to increase your data points to make the fit better.2. Create a vector y=exp(x). Now y should be ramdom numbers drawn from a log-normal
distribution. Fit y using the density function of log-normal distribution (dlnorm). Create
a vector y2 directly using rlnorm and fit it again.3. Create random numbers from gamma distribution (rgamma) and fit the density using the
same method.4. In the above question 1, try to add another density line by using lines(xfit,dnorm(xfit,mean=mean(x),Compare it with the theoretical density line. Can you see any di↵erence? Increase the
data points and try again. Try to explain the di↵erence between the two lines.• Download data “pepci.csv” and save it into your working directory.
• Extract recent 3-year daily prices, recent 5-year weekly prices, recent 10-year weekly prices
and 20-year quarterly prices.• For each of the four time series, calculate simple returns and log returns for both overlapping and non-overlapping types.
• Draw histograms of the all returns. Are they normal?
• Feel free to use any package in this question.In high frequency trading, the data format is di↵erent from other intraday data. Instead of
open, high, low, close, you would see bid price, ask price and trade price. Bid price is the price
trader want to sell at market, ask price is the price trader want to buy from market, trade price
is the price at which stock are sold or bought.Read AAPL.O.csv and do the following questions;
1. Create a table which contains: Date.L., Time.L., Type, Price, Volume, Bid.price, Bid.Size,
Ask.Price and Ask.Size
2. Create a column and name it as Trading.Time. For this column, you have to combine
Date.L. and Time.L together, then put this column to the table you created in step 13. Subtract all the rows, which marked as Quote in Type column. Name this table as
AAPL.Quote. Also create a table which only contains Trade, name this table as AAPL.Trade4. Calculate time di↵erence for each row and save it as numeric vector, unit should be minute5. Calculate spread between bid price and ask price. Make a histogram for spread6. Make a line chart for AAPL.Trade, use time in x-axis, volume in y-axis.