Suppose X(adsbygoogle = window.adsbygoogle || []).push({}); _{n}is a random variable. Let b and c be a constant.

Is the following generally true?

[tex]P(|X_{n}-b| \geq \epsilon) = P(|X_{n}-b|^{2} \geq \epsilon^{2}) [/tex]

This says that the probability that Xn minus b is greater than or equal to epsilon is equal to the probability that Xn minus b squared is greater than epsilon squared.

My prof keeps saying that they are the same event, therefore, they have the same probability. But I still don't understand. Any insight?

Thanks,

M

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# Is this equality generally true? | Probability

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