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

On Monday, June 17, 2013 1:12:51 PM UTC-4, fl wrote:
> 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
1( ) is the indicator function which is equal to 1 when its argument is true, and 0 otherwise.
E[1(X>t)] is a fancy way of writing P[X>t] which is the probability that the random variable X exceeds a certain t. 

Writing probabilities as an expected value of an indicator function is a common trick used in probability theory.