An affine image of a standard normal

Topic: Functions of random variables and limit theorems · more questions on this topic
‹ The square of a uniform variable Two standard normal probabilities ›

Let X\sim\operatorname{N}(0,1) and Y=1+2X. What is the distribution of Y?

Worked answer (click to show)

An affine image of a normal variable is normal. The mean is 1 and the variance is 4, so Y\sim\operatorname{N}(1,4).