Anyone can help me to check my answer(in my first reply)? Thanks

For any event A, A is a subset of the sample space S.

show that E(IA) = P(IA = 1) = P(A).

IA is Indicator random variable

Question

Anyone can help me to check my answer(in my first reply)? Thanks

For any event A, A is a subset of the sample space S.

show that E(IA) = P(IA = 1) = P(A).

IA is Indicator random variable

anonymous · Answer

If $$A$$ is event occurs, $$I_{A} = 1$$ So $$I_{A} = 0$$ is event Not occurs, then

$$E(Y) = \sum_{y} y P(Y=y) | y=0,1 $$
$$E(Y) = 0P(Y=0) + 1P(Y=1) = P(Y=1)$$

As we know from Bernoulli distribution $$P(I_{A}=1) = P(A)  \and\ P(I_{A}=0)   = 1 - P(A)$$
Then 
$$E(I_{A}) = P(I_{A}=1) = P(A)$$

anonymous · Answer

Hi @dumbcow , Sorry to bother you again, could you please help me check my answer again for this new question?

dumbcow · Answer

everything looks correct to me...you may want a 2nd opinion just to confirm it

anonymous · Answer

Thanks @dumbcow, you are really helpful. I will leave this open to see if others would like to comment.

anonymous · Answer

looks good to me!

anonymous · Answer

Thanks @pgpilot326 , I can close this question now :)