# Math Help - Discrete or continuous?

1. ## Discrete or continuous?

The shelf life, in days, for bottles of a certain medicine is a random variable that has the density function

$
f(x) = \frac{20000}{(x+100)^3}, x > 0$

0, elsewhere

What is the probability that a bottle of this medicine will a shell life of
atleast 200 days?

My professor said that this is a continuous random variable and gave this integral: $\int^{\infty}_{200} \frac{20000}{(x+100)^3} dx =
\frac{-10000}{(x+100)^2}$
from 200 to infinity

I say the random variable is discrete because the number of days is countable.

2. It's certainly a continous random variable.
That is a valid density.
However, the number of days of anything should be a discrete rv.
Hence that density may not be appropriate in this setting.
To make you both winners it should say that the distribution of days is APPROXIMATELY....