What is E[1(X>t)]?

Hi,

When I read wiki on importance sampling:


http://en.wikipedia.org/wiki/Importance_sampling


I do not understand the meaning of:

E[1(X>t)]

Could you explain it to me?

Thanks

ruwan2 said:

Hi,

When I read wiki on importance sampling:


http://en.wikipedia.org/wiki/Importance_sampling


I do not understand the meaning of:

E[1(X>t)]

Could you explain it to me?

Thanks

Click to expand...

I can guess! An expectation value has to be a number. The "1" means the numeric value 1 is given to an event if the logical expression (X>t) is true, 0 otherwise. Then it follows that the expectation value is the number of successes divided by the number of trials, which is one way to define the probability \(\displaystyle p_t\).