4.6 Deviation: Markov & Chebyshev Bounds

Markov Bound


Given a random variable \(R\) with \(E[R] = 50\), give the smallest value \(x\) such that the Markov Bound guarantees \( \Pr[R \geq x] \leq 0.5\) under the following conditions. If the Markov bound cannot be applied, enter 6042.

  1. \(R\) is non-negative

    Exercise 1


  2. \(R\geq -50\)

    Exercise 2


  3. \(R\geq 30\)

    Exercise 3


  4. \(Pr[R \leq 50]=0.7\)

    Exercise 4