C？假设每天的温度是独立的。

25岁和35岁以上，35岁以上的女性）及其受教育程度（小学，中学，大专）。基于

25至35 10 20 15之间

Question 1. For numerical data, what is the difference between the measurement scale of interval and the
measurement scale of ratio? Give an example of numerical data whose measurement scale is ratio.

Question 2. The following table shows the frequency distribution in terms of relative frequency of daily
temperatures in November in New South Wales. What is the probability that the temperature of two
consecutive days exceeds 20o
C? Assume daily temperatures are independent.

Temperature Relative frequency

Question 3. There are 50 coloured balls (10 red balls, 15 yellow balls, 20 purple balls, 5 blue green balls)
in a box. If we would like compute the probability that there are exactly 3 yellow balls out of a random
selection of 5 balls, can we use the binomial distribution. Explain why / why not.

Question 4. There are two stocks an investor can invest in. The expected rate of return is the same for both
Stock A and Stock B. Without using any maths, explain why for a risk-averse investor she would like to
choose a stock whose returns have a smaller inter-quartile range.

It is of interest to know the dependence structure between age of first marriage (younger than 25, between
25 and 35, older than 35) of females and their education attainment (Primary, Secondary, Tertiary). Based
on the following incomplete contingency table, answer Question 5 and Question 6.

Primary school Secondary school Tertiary school Total
Younger than 25 30 5 60
Between 25 and 35 10 20 15
Older than 35 15 70
Total 50 175

Question 5. Suppose a woman aged 37 just got married the first time. What is the probability she has tertiary
education?

Question 6. The 𝜒𝜒2 statistic used to test whether or not age of first marriage and education attainment are
independent equals 37.8263. At the 5% level, what is the critical value and what is the test result?

Question 7. The Poisson distribution has one property that is sometimes referred to as “Poisson arrivals
see exponential waiting time”. What does it mean?

Question 8. It is known that the number of vehicles passing through a roundabout follows a Poisson
distribution. On average during a single off-peak hour, 20 vehicles pass through the roundabout; whereas
on average during a peak hour, number of vehicles that pass through the roundabout doubles. What is the
probability that during a peak hour, after one vehicle passes the roundabout one needs to wait between one
minute and three minutes to see the next vehicle?

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