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Homework Statement
Show that the exponential distribution has the memory loss property.
Homework Equations
[tex]f_T(t) = \frac{1}{\beta}e^{-t/\beta}[/tex]
The memory loss property exists if we can show that
[tex]P(X>s_1+s_2|X>s_1) = P(X>s_2)[/tex]
Where
[tex]P(X>s_1+s_2|X>s_1)=\frac{P(X>s_1+s_2,X>s_1)}{P(X>s_1)}[/tex]
The Attempt at a Solution
For [itex]P(X>s_2)[/itex] I computed the integral
[tex]1-\int_0^{s_2}f_T(t)dt[/tex]
And similarly I found [itex]P(X>s_1)[/itex] but I'm unsure how to find [itex]P(X>s_1+s_2,X>s_1)[/itex] to complete the problem.