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trying to fixed aligned 2E1
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paul-laskowski authored Feb 2, 2024
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10 changes: 5 additions & 5 deletions _problems/unit-02/E-cdf-of-a-continuous-rv/1.md
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Expand Up @@ -15,11 +15,11 @@ Let F(x) be the CDF of X. Based on the given information, $F(x) = 0$ for $x \le
For $x \ge 0$, $F(x)$ can be found as the following

$$\begin{aligned}
F(x)&= \int_{-\infty}^x \frac{u}{2}du \\
&= \int_{-\infty}^0 f(u)du + \int_{0}^x f(u)du \\
&= 0 + \int_{0}^{x}\frac{u}{2}du\\
&= \frac{x^2}{4}\\
\end{aligned}$$
F(x)&= \int_{-\infty}^x \frac{u}{2}du \\\\
&= \int_{-\infty}^0 f(u)du + \int_{0}^x f(u)du \\\\
&= 0 + \int_{0}^{x}\frac{u}{2}du\\\\
&= \frac{x^2}{4}
\\end{aligned}$$

(b) $$\begin{aligned}
P(X<1) = F(1) = \frac{1^2}{4} = \frac{1}{4}
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