Determine distribution of aX+b when X~N(0,1)
Company: Upstart
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: HR Screen
Let X ~ N(0,1). For constants a,b ∈ ℝ, define Y = aX + b. 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.
Quick Answer: This question evaluates understanding of affine transformations of the normal distribution, moment calculation, and probability density manipulation, measuring core competency in probability theory and mathematical statistics.