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Functions of a DRVAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

  • Formula for E(g(X))?
  • How do you find E(5X^3)?
  • How do you find E(18X^{-3})?
  • Is E(X^2)=[E(X)]^2?
  • Is E\left(\frac1X\right)=\frac{1}{E(X)}?
  • When does E(g(X))=g(E(X))?
  • Formula for Var(g(X))?
  • Var(kY)?
  • What is needed to find Var(5X^3)?
  • If two values of x give the same g(x), what do you do?
  • What does a table of x, g(x), p help with?
  • Variance of g(X) comes out negative. What is wrong?

Exam questions on Functions of a DRV

  1. The discrete random variable XX takes the values 1,2,31,2,3 with P(X=1)=0.2P(X=1)=0.2, P(X=2)=0.5P(X=2)=0.5 and P(X=3)=0.3P(X=3)=0.3.
    Find E(5X3)E(5X^3).2 marks
  2. The discrete random variable XX takes the values 1,2,41,2,4 with P(X=1)=0.4P(X=1)=0.4, P(X=2)=0.4P(X=2)=0.4 and P(X=4)=0.2P(X=4)=0.2.
    Hence find Var(6X−1)\mathrm{Var}(6X^{-1}).2 marks
  3. The discrete random variable XX has probability distribution P(X=x)=x10P(X=x)=\frac{x}{10} for x=1,2,3,4x=1,2,3,4.
    Find E(18X−3)E(18X^{-3}).3 marks
See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).