PLease show all steps reasonings TF Question FX is continuou

PLease show all steps (reasonings)****************

T/F Question:
F(X) is continuous with {-00. 00} is:

(a) F(x) > 0 for all x

(b) F(x) < 1 for all x

(c) F(x) is a continuous function

Thank you!

PLease show all steps (reasonings)**************** T/F Question: F(X) is continuous with {-00. 00} is: (a) F(x) > 0 for all x (b) F(x)

Solution

a) since probability can never be less than zero

F(X) >0

True

b)

similarly probability can never be greater than 1

F(X) < 1

True

c)

F( X) has discontunity , then the X become mixed continuous function

hence F(X) is continuous function

d)

F(X) contains all the events of sample space , hence , the cumulative probability must be equal to 1

hence true