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Hi all i have this question in which i don't really understand the line of reasoning.

Given rvs X ∼ N(0, 1), Y ∼ N(0, 4), is P(X > 3) < P(Y < –6)?

The reasoning is :

P(Y < –6) = P(Y > 6) < P(Y / 2 > 3) = P(X > 3).

I don't understand this part: P(Y > 6) < P(Y / 2 > 3)

Isn't P(Y / 2 > 3) exactly equal to P(Y > 6)?

Also i don't really understand why P(Y / 2 > 3) = P(X > 3)

Could anyone enlighten me?

Thanks :)

1 Answers 1