Determine whether each of the following functions could be a

Determine whether each of the following functions could be a CDF over the indicated part of the domain:

a) F(x)=e^-x on 0 <= x < infinity

b) F(x)=e^x on -infinity < x <= 0.

c) F(x)=1-e^-x on -1 <= x < infinity.

Solution

Note that cdf has a value of 0 at the start of the domain, and 1 at the end of the domain.

a)

If F(x) = e^-x,

F(0) = 1
F(oo) = 0

Hence it cannot be a cdf.

b)

F(x) = e^x

F(-oo) = 0
F(0) = 1

Hence, IT CAN BE a cdf.

c)

F(x) = 1 - e^-x

F(-1) = 1 - e
F(oo) = 1

Hence, it cannot be a cdf.