Cumulative distributions
A continuous random variable X that can assume values between 0 and 1 has a cumulative distribution given by:
\[ \begin{align}
F(x) &= \frac{x^2+4x}{5} \quad 0 \le x \le 1 \\
&= 0 \quad x \lt 0 \\
&= 1 \quad x \gt 1
\end{align}\]
(a) Find the corresponding probability density function.
(b) What is the probability of X taking a value less than 0.75?
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What is the relation between the cumulative distribution and the probability density function?
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