605_Discussion 8

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Chapter, Section 1 - Exercise 5:

Let X be a random variable with E(X) = 0 and V(X) = 1. What integer value k will assure us that \(P(|X| \geq k) \leq .01\)?

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Given:

• E(X) = 0
• V(X) = 1

Using Chebychev’s Inequality:

\[P(|X-\mu| \geq k\sigma) \leq 1/k^2 \] \(\mu = 0\) and \(\sigma = 1\), \[P(|X| \geq k) \leq 1/k^2 \] => \(1/k^2 = .01\) => \(k = \sqrt{1/.01}\)

k <- sqrt(1/.01)
cat(sprintf("%s = %f \n", c(" k"), c(k)))

##  k = 10.000000