4-17. Comment on the following statement: IfXis a continuous random variable, then its probability density function need not be continuous; however, its cumulative distribution function will be continuous. Let f (x) = -13

, x ∈ {0 < x < 1} ∪ {4 < x < 6};

0 elsewhere.

Is f discontinuous over its domain? If so, where? Can f serve as a probability density function?

(Hint: 4xεA∪B f (x)dx = 4xεA f (x)dx + 4xεB f (x)dx.)