Generate Samples from Truncated Normal Distribution

Q: Generate Samples from Truncated Normal Distribution

This question evaluates understanding of truncated normal distributions, including the probability density and cumulative distribution functions, and the competency to reason about and implement sampling from a distribution conditioned on an interval.

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Question

Scenario

You draw from a normal distribution but only keep observations that are greater than 1 (i.e., values below 1 are discarded).

Assume the original variable is X ~ N(μ, σ²) and we keep only X ≥ 1. The special case μ = 0, σ = 1 corresponds to a standard normal.

Questions

What is the resulting distribution called?
Provide its formal PDF and CDF.
Describe at least two different ways to generate random samples directly from this truncated normal distribution. Inverse-CDF and rejection/Monte Carlo methods are acceptable.

Generate Samples from Truncated Normal Distribution

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Generate Samples from Truncated Normal Distribution

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