2.2.3 Survival Function Method Flashcards
(13 cards)
what does the survival function method do?
The survival function method is an alternative to the probability function method of calculating expected values.
what must be true abt the random variable in order to apply the survival function method?
the random variable’s range does not include any negative values
What’s the expected value formula using the survival function for discrete variables?
E[X] = sum from x = 0 to infinity of P(X>x)
What’s the expected value formula using the survival function for continuous variables?
E[X] = integral from 0 to infinity of S(x)dx
What’s the general survival-based expected value formula for any function ( g(x) )?
E[X] = integral from 0 to infinity of S(x) * g’(x) dx
What is the conceptual idea behind the survival function method?
Add up the probabilities that the random variable survives past each point — it’s a “stack of survival.”
How do you handle piecewise-defined survival functions for continuous variables?
Break the integral at each piece’s boundary and integrate each section separately.
What’s a common mistake when using the survival function method?
Forgetting to split the integral or sum when the survival function changes at different ranges.
Can the survival function method be used for mixed distributions?
Yes — by integrating or summing each segment separately based on the survival function.
What happens if the survival function has a constant section?
That portion contributes linearly to the integral — don’t forget to account for it!
Why can the survival function method be misleading in discrete cases?
Because it uses integrals that must be split into piecewise sums — not as clean as continuous.
What’s one last warning when using the method?
You must make sure the survival function is correct at each interval — or everything falls apart.
how should you use the survival function method for when X is defined for a ≤ X ≤ b?
Discrete: E[X] = a + sum from x=a to b - 1 of P(X>x)
Continuous: E[X] = a + integral from a to b of S(x)dx
