Continuous Random Variables

Question 1

How to get from a p.d.f. to a c.d.f. and vice versa?

Answer 1

p. d.f. -> c.d.f. - Integrate

c. d.f. -> p.d.f. - Differentiate

Question 2

What is a mode?

Answer 2

The mode is the value of the random variable where it is most dense i.e. where the p.d.f. reaches its highest point. So to find mode d/dx f(x)=0

Question 3

What is E(aX+b) and Var(aX+b)?

Answer 3

E(aX+b) = aE(X)+b
Var(aX+b) = a^2 Var(X)