There are just two requirements:
1) and
2) .
The continuous random variable X has a probability density function defined as follows:
f(x)= 1/4 , 0<=x<1,
= 3/8 (3-x) , 1<=x<=3
The pdf is not continuous at x=1 and probability density functions are only defined when they are a continuous function. So is the pdf given above valid?