[SOLVED] MATH255: Mathematics for Computing Assignment 2

This assignment is to be completed individually, with different randomly generated data sets for each student. You may hand-write or type your answers, but the Moodle submission link will accept a .pdf file only, plus a .txt file for R code. Whether your working out is done by hand, in R or both, it must be handed in. Unless otherwise stated, three significant digits is enough for all your answers, so for example a probability of 0.4386 can be given as 0.439. The assignment is due Friday Week 12 at 11:30pm.

1. Generate 10 random points (x_i,y_i) restricted by x_i ∈ [−2,2] and y_i ∈ [0,4], rounded to one decimal point. Save your data set; you will need to submit it along with the rest of your work. Here is an example:

• Load your data into R and make a scatterplot with x on the horizontal axis. Put the best-fit line on the graph.
• Calculate the correlation coefficient and find the equation of the best-fit line.
• Do you believe your variables are significantly correlated? Explain. Is this what you would expect, given the manner in which the data set was created?

2. You run an experiment in which you roll a fair die repeatedly until you roll a 6 and observe how many rolls were required. You play this game 100 times and record the 100 observations.
   • What type of distribution does this data set have? Using the particular number for probability of success in this case, write the pdf and cdf formulas.
   • What is the probability that it takes you between 5 and 8 trials to roll a 6?
3. A dispenser in a shopping centre releases on average 25 grams of jelly beans for a dollar. The weight released is normally distributed with variance 2 grams. If the machine is used 250 times in a week, about how many of those times will it release less than 23 grams?
4. It is observed that an average of 7 out of every 10 diners at a restaurant order dessert after their meal. 20 diners are selected at random and polled.
   • Calculate the probability that 12 of them had dessert.
   • Calculate the probability that fewer than 17 of them had dessert.
5. Construct a linear continuous pdf = 0 and demonstrate that it is a pdf, i.e. show that f(x) ≥ 0 for all x ∈ domf and = 1. Draw the graph of the

function and indicate its domain. Calculate the IQR of your function.