- #1
magnifik
- 360
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For X ~ N(μ, σ), what is P[|X-μ] < σ] in terms of the Q function?
I know that P[|X-μ] < σ] can be decomposed into P[X > -σ + μ] + P[X < σ + μ] I'm not sure what to do next. i know P[X < σ + μ] can be expressed as 1 - phi(σ + μ - μ / σ) = Q(1), but I'm not sure how to approach P[X > -σ + μ]. I know the answer is 1 - 2Q(1)...not sure where this all comes from
I know that P[|X-μ] < σ] can be decomposed into P[X > -σ + μ] + P[X < σ + μ] I'm not sure what to do next. i know P[X < σ + μ] can be expressed as 1 - phi(σ + μ - μ / σ) = Q(1), but I'm not sure how to approach P[X > -σ + μ]. I know the answer is 1 - 2Q(1)...not sure where this all comes from