Discrete Mathematics
# Continuous Random Variables

**Details and Assumptions**

- A survival curve plots the fraction of survived patients according to elapsed time.
- \(a=\frac{1}{324}\) and \(b=\frac{1}{23}.\)
- The figure is not drawn to scale.

Suppose that the life expectancy \(X\) of a cat species has the probability density function \[f(x)=kx(x-20)\] for \(0\leq X\leq20.\) John the farmer decided to breed this species, and bought hundreds of these newborn cats. If John currently has \(2000\) cats, all of which are \(10\) years old, how many of these cats will die before becoming \(14\) years old?

**Note:** Ignore reproduction of the cats.

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