This question came up this week when I had to put my rice in the microwave for a third time.
Suppose the perfect cooking time for a meal is given by a random variable $X$ with values in seconds. Now suppose a quick check allows to determine if the food is :
- Uncooked,
- Perfectly cooked,
- Overcooked.
What is the estimated overcooking time in seconds if one uses the following technique :
Start by cooking for $T$ seconds, then
a) Check food state.
b) If food if perfectly cooked or overcooked, stop.
c) If food is uncooked, double the last $T$ used.
An answer could also hint for a better technique or optimize the choice of $T$.
EDIT : As suggested bellow, let us assume that $X\sim N(\mu;\sigma^2)$.