# Thread: continuous random variable

1. ## continuous random variable

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?

2. There are just two requirements:
1) $\displaystyle f(x)\ge0$ and

2) $\displaystyle \int_{ - \infty }^\infty {f(x)dx} = 1$.

3. Originally Posted by hooke
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?
No they are allowed to be discountinuous. The requirement is that it be positive, (Lebesgue) integrable, and integrate up to 1.

CB

4. Originally Posted by CaptainBlack
No they are allowed to be discountinuous. The requirement is that it be positive, (Lebesgue) integrable, and integrate up to 1.

CB
Thanks CB and Plato, how about the cummulative distribution function? Must it be continuous?

5. Originally Posted by hooke
Thanks CB and Plato, how about the cummulative distribution function? Must it be continuous?
Yes, its a consequence of the defining integral.

CB