Update 1.md

Author: koohong

_problems/unit-03/B-expectation-of-a-continuous-random-variable/1.md

@@ -1,5 +1,8 @@
 ---
 index: 1
 statement: 
-$$X(x) = \begin{cases} 1, &x \le 2\\\\ 2, &otherwise\end{cases}$$:
+Pdf of X is defined as the following
+$$f(x) = \begin{cases} x for x \le x \e 1, &1-x \le 1 x le 2, &otherwise\end{cases}$$:
 ---
+
+$E[X] = \int_0^1x \cdot x dx + \int_1^2 x(2-x)dx = \frac{1}{3} + \frac{2}{3} = 1$