diff --git a/_problems/unit-03/B-expectation-of-a-continuous-random-variable/1.md b/_problems/unit-03/B-expectation-of-a-continuous-random-variable/1.md index ccf5617..e549734 100644 --- a/_problems/unit-03/B-expectation-of-a-continuous-random-variable/1.md +++ b/_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 +$$f(x) = \begin{cases} x for x \le x \e 1, &1-x \le 1 x le 2, &otherwise\end{cases}$$: --- + +$E[X] = \int_0^1x \cdot x dx + \int_1^2 x(2-x)dx = \frac{1}{3} + \frac{2}{3} = 1$