manipulating random variables

Question 1

Transformations of Random Variables

Answer 1

Question 2

basics of CDF/PDF:

Answer 2

Question 3

Answer 3

Question 4

Transforming the pdf directly

Answer 4

An alternative way to find the pdf directly is by change of variables.

We present this for completeness and for anyone who prefers it as a method. Our observation is that most people find the cdf easier to transform.

In calculus you learned the ‘u’-substitution. We’ll do a calculus example to remind you how this goes and then apply it to the pdf.

Question 5

Answer 5