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3 marksProbability, Probability Distributions and Regression

CAPE Integrated Mathematics · 2016 · Paper 2 · Question 3(d)(ii)

The probability density function for a discrete random variable X with mean E(X) = 2.7 is given in the table.

Find the variance, Var(X).

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  1. 3(a)(i)Identify the type of sample if the psychologist assigns each student a number from 1 to 3960, randomly chooses one of the first 132 numbers, and selects every…[1 mark]
  2. 3(a)(ii)Identify the type of sample if the psychologist assigns each student a number from 0001 to 3960 and uses a computer to randomly generate a list of 30 numbers…[1 mark]
  3. 3(a)(iii)Identify the type of sample if students are listed by neighbourhood, 6 neighbourhoods are randomly selected, and all students from those neighbourhoods form…[1 mark]
  4. 3(a)(iv)Identify the type of sample if an equal proportion of students is randomly selected from each of the 5 departments at the college.[1 mark]
  5. 3(b)(i)Calculate the mean height for the 51 children.[4 marks]
  6. 3(b)(ii)Calculate the standard deviation of the heights for the 51 children.[5 marks]
  7. 3(c)(i)A team of 3 girls and 3 boys is to be chosen from a group of 6 girls and 5 boys to represent its class at a mathematics competition. Find the number of ways in…[3 marks]
  8. 3(c)(ii)Sarah and Hannah are in the group of 6 girls. Find the number of ways in which the team may be chosen if neither Sarah nor Hannah is on the team.[3 marks]
  9. 3(d)(i)Show that a = 3.[3 marks]

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