An affine image of a uniform variable

Topic: Functions of random variables and limit theorems · more questions on this topic
‹ A quadratic function of a uniform variable A normal law with mean 2 ›

Let X be uniform on [1,3] and set Y=4X+5. What is the distribution of Y?

Worked answer (click to show)

Y is uniform on [4\cdot 1+5,\,4\cdot 3+5]=[9,17].