Schedule for week 4

Homework

homework4.Rmd: All answers to the questions, codes and results (figures, tables) should be included in this single file.

  1. Generate the mathematical notations listed in https://www.calvin.edu/%7Erpruim/courses/s341/S17/from-class/MathinRmd.html.
  2. Generate 100 random numbers from uniform distribution ranging from 0 to 10.
    • Draw the histogram of the numbers.
    • Compute the mean, median, variance, and standard deviation of these numbers.
  3. Generate 100 random numbers from normal distribution with mean 10 and standard deviation 2.
    • Draw the histogram of the numbers.
    • Compute the mean, median, variance, and standard deviation of these numbers.
  4. Coint toss simulation:
    • Simulate 100 random coin tosses for a fair coin, using the sample function. How many heads do you get? How many do you expect to get?
    • Repeat the above (100 random coin tosses) for 1000 times, that is, in a trial, you toss the coin for 100 times and record the number of heads. You do it again and again for 1000 times (so in total you’ll toss the coin for 100,000 times). At the end, you will have 1000 numbers (for the numbers of heads in each trial). You can do this in a loop, and call sample function in the loop.
    • Draw the histogram for the numbers of heads from all trials. Does it look similar? Yes, it looks like the bell-shaped curve (normal distribution). This is the amazing law of the large number, i.e., the means of a group of numbers (whatever it is) converges to a normal distribution.
  5. Dice rolling simulation:
    • Assume you have a fair dice (six sides with numbers 1-6). Simulate 100 dice rolling, using sample function. Report the number of times you see each side (using the table function).
    • Assume you have two fair dice. You roll them at the same time and record the sum of the numbers from both dice. Simulate 100 such throwing, and report the numbers you get.
  6. Based on the mtcars data frame,
    • Generate one figure with 2 panels for mpg vs hp and mpg vs wt. I expect to see a figure like the following

    • Use different colors in the above figure for cars with different numbers of cyl. I want you to play with different color options, but finally use some transparent color in solid points (hint, the point type is pch=19). I expect to see something like the following (colors don’t have to be exactly the same):

    • Generate a figure with 4 panels in a 2x2 layout. I expect to see a figure like the following:

  7. Put math expression in figures. Generate a figure for power function . Show the curves for k=0.5, 1, 1.5 in the same figure. In the figure, You should:
    • show all 3 lines with different colors. You can check out the matplot function to draw multiple lines together.
    • Use log scale for y-axis. Hint: this can be achieved by specifying log="y" in the plot.
    • Use math expression as axis labels.
    • Provide legend for lines.

    The following codes will get you started. But you need to modify the parameters in the matplot function.

     x = 1:100
 y1 = x^0.5
 y2 = x^1
 y3 = x^1.5
 matplot(x, cbind(y1, y2, y3), type="l", lty=1, log="y", lwd=2)

    I expect to see a figure like the following:

Day 1: Review

Day 2: Random number generator in R

Day 3: Random number generator in R

Day 4: A little bit more advanced R base graphics

Day 5: Review

Review all contents for this week, especially the day 2 and 3 stuff. The simulation question in the homework might be a little complicated. Talk to me if necessary.