Math topic中文

Linear combination

Solving problems involving the use of $\mathrm{E}(aX+bY)$ and $\mathrm{Var}(aX+bY)$ , where $X$ and $Y$ are independent.

Practice questions

1Section B: Statistics [60 marks] A manager claims that the time spent by each customer at his supermarket follows a norm…
2In this question you should state the parameters of any distributions that you use. Crispy Cream Donut Shop sells 2 type…
3 $X$ is a normal random variable with mean 1 and variance 1, and $Y$ is also a normal random variable with mean $\mu$ and…
4A credit card company has a special 24-hour telephone hotline for customers to either report a lost credit card or to re…
5Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
6In this question, you should state clearly all the distributions that you use, together with the values of the appropria…
7S and T are independent random variables with the distributions $N(18,3^2)$ and $N(\mu,\sigma^2)$ respectively. It is gi…
8**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
9Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
10In this question you should state clearly the values of the parameters of any normal distributions that you use. The mas…
11In this question you should clearly state the values of the appropriate parameters of any distributions used. The diamet…
12The mass, $X$ grams, of soup packed into a can by machine $A$ is normally distributed with mean $\mu$ grams and standard…
13In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieties,…
14The probability of obtaining a head when a particular coin is tossed is $p$ . A fair cubical die has the number '1' on on…
15The average number of calls per hour received by telephone operators at the Call Centre of bank ECBC is being reviewed.…
16A nursery supplies plants to Evergreen Pte. Ltd. The heights, in centimetres, of plants supplied may be taken to follow…
17[For this question, you should state clearly the values of the parameters of any normal distribution you use.] After din…
18The masses, in grams, of the packets of semolina flour follow the distribution $N(225,\;25^2)$ and the masses, in grams,…
19In this question you should state clearly the parameters of any normal distributions you use. The masses in kilograms of…
20To reduce the number of speeding incidents on the road, traffic police in Country S set up traffic cameras at 3 busy tra…
21A policeman inspects each passenger in the car that he stops during a roadblock. The number of passengers in a randomly…
22A credit card company has a special 24-hour telephone hotline for customers to either report a lost credit card or to re…
23Green Earth Factory produces solar panels. On average, 2% of the solar panels produced are found to contain defects. The…
24In this question you should state the parameters of any distribution you use. A customer service call centre categor…
25During the Great Mega Sale, the waiting times, in minutes, for men and women, at their respective fitting rooms, have me…
26In a school canteen, the number of people joining the noodle stall queue in a period of 30 seconds is a random variable…
27In this question, you should state the parameters of any distribution that you use. A local fish market is famous for tw…
28At the drinks stall in a canteen, both hot and cold drinks are sold. The number of hot drinks sold per minute follows a…
29**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
30In this question, you should state clearly the distribution of any random variables that you define. The volume, $S$ , in…
31In this question you should state the parameters of any normal distributions that you use. A petrol station (Station $A$ …
32In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
33Good Papa Caf'e sells only two types of muffins, chocolate and banana. The number of chocolate and the number of banana…
34A factory manufactures paperweights consisting of glass mounted on a wooden base. The volume of glass, in $\text{cm}^3$ ,…
35Epple Company manufactures a large number of E-phones. It is known that 1% of the E-phones manufactured are defective. A…
36In this question you should state clearly all the distributions that you use, together with the values of the appropriat…
37**In this question you should state clearly all the distributions that you use, together with the values of the appropri…
38A grocery store sells two types of apples, Brand $A$ and Brand $S$ . The masses (in grams) of the apples for each brand c…
39Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
40In a Junior College, the Physical Education (PE) department is analyzing the running time taken by girls from 2 cohorts,…
41The speeds of an e-scooter ( $X$ km/h) and a pedestrian ( $Y$ km/h) measured on a particular stretch of footpath are norma…
42In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieti…
43In this question you should state the parameters of any distributions that you use. To regulate the use of its facil…
44'Famous Amas' makes two types of cookies, almond cookie and chocolate chip cookie. The mass of an almond cookie and a ch…
45Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
46Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
47In an examination, the score, $X$ , for paper 1 of a student is found to follow a normal distribution with mean 62 and st…
48In this question you should state clearly the values of the parameters of any normal distributions you use. A fruit…
49In this question you should state the parameters of any distributions you use. A snack company produces two types of…
50In this question you should state the parameters of any distributions that you use. To regulate the use of its facilitie…
51A supermarket sells boxes of a particular brand of biscuits in two flavours, chocolate and strawberry. The mean number o…
52The table below shows the BMI-for-age for boys aged 18 years in Singapore. | Age (years) | Weight Indicator | Underweigh…
53Fruits are sold by weight. Apples are sold at $2 per kg and oranges at $3 per kg. The masses, in kg, of apples and ora…