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![[tex]F_{X}(x)= (1 - e^{-x}) 1\{0 \le x \le 1\} + 1\{1 \leq x\} [/tex]](images/latex/a62bb4aa88a4b184833f62d726faccb896b58b70_0.png "[tex]F_{X}(x)= (1 - e^{-x}) 1\{0 \le x \le 1\} + 1\{1 \leq x\} [/tex]")
. Hallar ![[tex]E(X|X>ln(2))[/tex]](images/latex/bcdcb40b7ce10e2a5320cc523f4d5717f239a5d8_0.png "[tex]E(X|X>ln(2))[/tex]")
![[tex]f_{X|X>ln(2)}(x)= \frac{ f_{X}(x) }{P(X>ln(2))} = 2 e^{-x} 1\{ln(2)\le x\le 1\}[/tex]](images/latex/200d6b3db4e6d6c5d1f2e2594d848da34a58707c_0.png "[tex]f_{X|X>ln(2)}(x)= \frac{ f_{X}(x) }{P(X>ln(2))} = 2 e^{-x} 1\{ln(2)\le x\le 1\}[/tex]")
![[tex]E(X|X>ln(2))= \int_{ln(2)}^{1} x 2 e^{-x} dx [/tex]](images/latex/7351081cf8cab2e6dd6dccd179337bcb150f0caf_0.png "[tex]E(X|X>ln(2))= \int_{ln(2)}^{1} x 2 e^{-x} dx [/tex]")
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