So many students have been asking for more practice. I’ll put up all the Prelim Papers for 2016 here. Do note that the syllabus is 9740 so students should practice discretion and skip questions that are out of syllabus. 🙂

(c) In how many ways can 5 copies of a book be distributed among 10 people if each person can get any number of books?

Notice that the difference between (b) and (c) is that the book distributed is not identical. So for (c), we are pretty much distributing identical balls to distinct boxes. Whereas for (b) , we are pretty much distributing distinct balls to distinct boxes.

A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears times (), he wins $ . If his number fails to appear, he loses $1. Calculate the gambler’s expected winnings

Comments/Explanations: The integration by parts can be really tedious. so just be careful. As for the part, it can be both -1 or 1, depending on what n is. So we have two values of a.

(ii)
The sample collected will be representative of the employee’s gender and department, instead of their age. Thus, it will not be suitable as it is not representative.

(iii)
Let be the age of employees.
Let be the population mean age of employees

(ii)
The scatter diagram shows a curvilinear relationship between x and y variables. Thus, a linear model is not appropriate.

(iii)
d is positive since it represent the maximum efficiency obtained as the power increases.
c is negative since the scatter show an increasing trend.

(iv)
Using GC,

(v)
When
The estimate would be reliable since it is within the data range. The value is close to 1 which shows a strong linear relationship.

(i)
The mean number of a particular type of weed that grow on the field is a constant.
A particular type of weed growing on the field is independent of another particular type of weed growing on the field.

(ii)
Let X be the number of dandelion growing per .