The Markov Inequality Let g(Y ) be a function of the

Chapter 4, Problem 198SE

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QUESTION:

The Markov Inequality Let \(g(Y)\) be a function of the continuous random variable 𝑌, with \(E(|g(Y)|)<\infty\). Show that, for every positive constant 𝑘,

                         \(P(|g(Y)|\le k)\ge1-\frac{E(|g(Y)|)}{k}.\)

[Note: This inequality also holds for discrete random variables, with an obvious adaptation in

the proof.]

Equation Transcription:

Text Transcription:

g(Y)

E(|g(Y)|)<infinity

P(|g(Y)|</=k)>/=1-E(|g(Y)|) over k.

Questions & Answers

QUESTION:

The Markov Inequality Let \(g(Y)\) be a function of the continuous random variable 𝑌, with \(E(|g(Y)|)<\infty\). Show that, for every positive constant 𝑘,

                         \(P(|g(Y)|\le k)\ge1-\frac{E(|g(Y)|)}{k}.\)

[Note: This inequality also holds for discrete random variables, with an obvious adaptation in

the proof.]

Equation Transcription:

Text Transcription:

g(Y)

E(|g(Y)|)<infinity

P(|g(Y)|</=k)>/=1-E(|g(Y)|) over k.

ANSWER:

Solution:

Step 1 of 1:

      Let g(Y) be a function of the continuous random variable Y, with

         To show that for every positive constant k,

                               

            Then,

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