The number of items produced in a factory during a week is known to be a random variable with mean 50 ● Using Markov's inequality, what can you say about the probability that this week's production exceeds 75? ● If the variance of one week's production is equal to 25, then using Chebyshev's inequality, what can be said about the probability that this week's production

The number of items produced in a factory during a week is known to be a random variable with mean 50 ● Using Markov's inequality, what can you say about the probability that this week's production exceeds 75? ● If the variance of one week's production is equal to 25, then using Chebyshev's inequality, what can be said about the probability that this week's production

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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A child gets a weekly allowance (a certain non-negative number of dollars). The amount (in dollars) is random with expectation equal to 6 and variance equal to 6. Let’s denote this random variable by X. I want to estimate (from above) the chances that the child gets 10 dollars or more on a given week. In other words, I want to find c such that P(X ≥ 10) ≤ c, with c that is as small as possible.(a) Use the Markov inequality to find c such that P(X ≥ 10) ≤ c.(b) Use the Chebyshev inequality for the variance to find c such that P(X ≥ 10) ≤ c.(c) Read about the one-sided Chebyshev inequality, and use it to find c such that P(X ≥ 10) ≤ c.
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