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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q47 Marks

In a probability distribution the random variable X takes the values −1, 0, 1, 2, 4. The probability distribution table for X is as follows. X -1 0 1 2 4 P(X = x) 1/4 p p 3/8 4p

  1. (i)Find the value of p.[2]
  2. (ii)Find E(X) and Var(X).[3]
  3. (iii)Given that X is greater than zero, find the probability that X is equal to 2.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [M1] Unsimplified sum of probabilities equated to 1
  2. [A1] p=1/16
  3. [M1] May be implied by use in Variance, accept unsimplified
  4. [M1] Substitute into correct variance formula, must have - 'their mean²'
  5. [A1] OE
  6. [M1] Conditional probability formula used consistent with their probabilities
  7. [A1] 6/11 or 0.545

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 1, question 4.

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