Introduction to Probability · Problem 8.2.15

Central Limit Theorem — Grinstead & Snell

Mathematics — Probability · law-of-large-numbers-continuous

Problem

Repeat Exercise 14, but this time with mean 10 and variance 3. Note that the table in Appendix A presents values for a standard normal variable. Find the standardized version X∗X^* for XX, find values for f∗(x)=P(∣X∗∣≥x)f^*(x) = P(|X^*| \geq x) as in Exercise 14, and then rescale these values for f(x)=P(∣X−10∣≥x)f(x) = P(|X - 10| \geq x). Graph and compare this function with the Chebyshev function g(x)=3/x2g(x) = 3/x^2.

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