Question

You have one dollar and a fair coin. If you get head, your position doubles but if you get tail, your position halves. What is the expected value of money after first toss?

  1. 5/4
  2. 1
  3. None

Answer

Expectation for a discrete event is defined as: \[\begin{aligned} E(X) &= \sum_{all x} x*p(x) \\ &= \frac {1}{2}*2 + \frac {1}{2} *\frac {1}{2} \\ &= \frac {5}{4} \end{aligned} \]

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