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4.7 Discrete random variables and expected valueIB Maths: Applications and Interpretation SL: Flashcards

What these 13 flashcards ask

  • What do the probabilities of a discrete random variable sum to?
  • Formula for the expected value of X?
  • What is a discrete random variable?
  • How can a distribution be given?
  • What does E(X) represent?
  • Must E(X) be a value X can take?
  • What does E(X)=0 mean when X is the gain of a player?
  • A game has expected gain -0.2 AED for the player. Who does it favour?
  • How do you find an unknown k in a distribution?
  • Find P(X\geq3) for x=1,\dots,4.
  • Gain in a game with entry fee 4 AED and prize X?
  • Expected total over 500 plays with expected gain g per play?
  • P(X=x)=\frac{4+x}{18} for x=1,2,3: P(X=1)?

Exam questions on 4.7 Discrete random variables and expected value

  1. The discrete random variable XX has the probability distribution P(X=1)=0.1P(X=1)=0.1, P(X=2)=0.3P(X=2)=0.3, P(X=3)=0.4P(X=3)=0.4 and P(X=4)=kP(X=4)=k.
    Find P(X≥3)P(X\geq3).2 marks
  2. The discrete random variable XX has probability distribution P(X=x)=x+418P(X=x)=\frac{x+4}{18} for x∈{1,2,3}x\in\{1,2,3\}.
    Find P(X≥2)P(X\geq2).2 marks
  3. At a fairground, a player pays 4 AED to spin a wheel. The prize is 0 AED with probability 0.5, 6 AED with probability 0.3 and 10 AED with probability 0.2. Let XX be the prize in AED.
    Find E(X)\mathrm{E}(X).3 marks
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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).