4.6 Deviation: Markov & Chebyshev Bounds

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

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2. \(R\geq -50\)

   Exercise 2

    Numerical Response 




3. \(R\geq 30\)

   Exercise 3

    Numerical Response 




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

   Exercise 4

    Numerical Response 

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