MAS1302: General Feedback on Assignment 1 Part A (non-computer questions) Generally well done by all those who made a serious effort.

 Question 1 (a) (Stem and leaf plot) Generally done well, although if there is no data for a particular ‘branch’ leave the branch blank; don’t miss it out! (a) (Stem and leaf plot) Generally done well, although if there is no data for a particular ‘branch’ leave the branch blank; don’t miss it out! (b) Mean and standard deviation: good, but remember for the standard deviation to divide by n-1, not n. (c ) 5-number summary: care needed with quartiles. (d) The main thing here was to notice the skew, and comment that the mean and standard deviation didn’t show it.

Question 2 The proof was either done well, or not at all. You should be able to do algebra like this without too much trouble though, so practice this one, and make sure you can! Question 3 (a) again, remember to divide by (n-1) in calculating the s.d. (b) make sure you multiply by the standard deviation, not the variance (s.d. squared). Questions 4, 5, 6 No general problems

Question 7 The starting point was the sequence from the congruential generator (mod 16): 13, 2, 7, … In order to convert each of these r i to an approximate U(0,1) observation u i, you were expected to divide each number by m=16. (This shows the importance of taking notice in lectures; I stopped *two* lectures in week 5 to explain this!) The u i are then put into the formula for the Geometric distribution. Remember that [x] means take the integer part of x, i.e. go to the next integer down. It does not mean round to the nearest integer! Questions 8, 9 No general problems

Part B: Computer Project  General comments: Once again, this was well done by all those who made a serious attempt.

Task 1 (Birthdays)  1. You were expected to list which days for each class had a shared birthday, and how many birthdays there were. Quote from marker: “Quite a few students just put in the tables of 1’s and 2’s to show me where the shared birthday was in a class, but the rows didn’t match up, so I couldn’t tell.”  2. Most people correctly noticed that the probability of at least one shared birthday increased with class-size, but a bit more detailed description of this increase was better.  3. A number of people didn’t really see what was happening: for class sizes of 23, the more classes we simulate, the more our estimated probability tends to zero in to the true value, which is close to 0.5.

Task 2 (Game-show problem)  Generally really well done.  A few students got a bit confused in part (c ): if this was you, check you understand it now.  You were meant to quote your estimated probabilities from your experiment for the probabilities of winning (i) when sticking and (ii) when switching. Don’t quote the theoretical (true) values (1/3 and 2/3) in this case!

Task 3 (Drawing pins)  Some students couldn’t get from the ‘npins’ table to the estimated probabilities – check you get this now!  The most common errors concerned the graph: incorrect labelling of axes, or not giving a title.