Problem 1: True or False - For each question answer whether the statement is true or false, and give a short explanation for your answer.

1. If ABc , then AB=
2. Let X be a random variable with cdf F(x), and Y a random variable with cdf G(x). If Y = X + 1, then G(x) F(x) for all x.
3. Let X and Y be the lifetimes of two different light bulbs (so X0 and Y0). If E[X] E[Y], then the hazard rate of X is larger than the hazard rate of Y for all x0
4. If f(x) is a pdf and g(x) is a pdf, then h(x) = max{f(x),g(x)} is a pdf. (For two numbers a and b, max{a,b} is the larger of a and b)
5. If P(AB)>P(ABc) , then P(AB)>P(A)