Determine distribution of aX+b when X~N(0,1)

Q: Determine distribution of aX+b when X~N(0,1)

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Question

Linear Transform of a Standard Normal

Setup

Let X ~ N(0, 1) (standard normal).
For constants a, b ∈ ℝ, define Y = aX + b.

Tasks

(a) What is the exact distribution of Y (name and parameters)?

(b) State its mean and variance.

(c) Does the sign of a affect the distribution parameters?

(d) What happens in the edge case a = 0?

(e) Write the pdf of Y explicitly.

Determine distribution of aX+b when X~N(0,1)

Linear Transform of a Standard Normal

Setup

Tasks

Solution (Locked)

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