Understanding Distribution Functions: Proving and Verifying Their Properties

[Alexsandro]

Could someone help me. I don't able to explain if is FG is a distribution fuction:
Show that if F and G are distribution functions and $0 \leq \lambda \leq 1$ then $\lambda.F + (1 - \lambda).G$ is a distribution function. Is the product F.G a distribution function?

 

[mathman]

In order see if a function is a distribution function, go back to the definition.

F(x) is a d.f. if F-> 1 as x -> inf, F-> 0 as x-> -inf. F(y)>=F(x) for y>x.

It should be easy for you to verify that in both examples you have a distribution function.