Math topic中文

Sample mean as random variable

Concept of the sample mean Xˉ\bar{X} as a random variable with E(Xˉ)=μ\mathrm{E}(\bar{X})=\mu and Var(Xˉ)=σ2n\mathrm{Var}(\bar{X})=\dfrac{\sigma^2}{n}.

Practice questions

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  2. 2Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  3. 3S and T are independent random variables with the distributions N(18,32)N(18,3^2) and N(μ,σ2)N(\mu,\sigma^2) respectively. It is gi…
  4. 4**In this question, you should state clearly all the distributions that you use, together with the values of the appropr…
  5. 5Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
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  7. 7Pat is invited to a game show. In the game, she is presented with a box with kk balls with either 1, 2, 3 or 4 printed…
  8. 8In this question you should state the parameters of any distributions you use. An orchard sells kiwis of two varieties,…
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  10. 10Alice uses a computer program to simulate 80 tosses of a biased coin. Let YY be the random variable denoting the number…
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  12. 12Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  13. 13Based on observations over a long period, the mean time taken by male students in Griffles Junior College (GJC) to compl…
  14. 14In a small town, there are two clinics, Lee's Clinic and Hope Clinic. At Lee's Clinic, the waiting time of a patient fol…
  15. 15A factory manufactures paperweights consisting of glass mounted on a wooden base. The volume of glass, in cm3\text{cm}^3,…
  16. 16**In this question you should state clearly all the distributions that you use, together with the values of the appropri…
  17. 17Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  18. 18One round of a game is played by randomly moving the counter from the starting point XX to one of the ending points AA…
  19. 19Fishing Company A has two types of fishing vessels, the "Standard" vessel and the "Large" vessel. The amount of fish cau…
  20. 20Students seeking admission to Kingdom University and Island University are required to apply using their national examin…
  21. 21A sample of nn observations was taken from a population of mean μ\mu and variance 10. Find the least sample size requi…
  22. 22An insurance company declares that the mean payment made on motor insurance claims is $10 000. The auditor examines a r…