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The Markov Inequality Let g(Y ) be a function of the
Chapter 4, Problem 198SE(choose chapter or problem)
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,