I need some help with "law of total expectation".(adsbygoogle = window.adsbygoogle || []).push({});

Sorry for my English, I don't know the right English expressions.

The Problem is:

People come (show in) with with Poisson rate of 10 people per hour.

There is a 0.2 chance that a person will give money to a beggar sitting in the corner.

The time that beggar is sitting is U[3,8] (continuous) hours.

Need to find the expectation E of people that will give money.

I mark:

N(t)~P(10*0.2*t) as the number of people giving money per hour.

X~U(3,8) time that beggar is sitting.

The given solution is following : E(N(X))=E(E(N(X)|X))=E(2X)=2*(3+8)/2

What I don't understand is their usage law of total expectation, according to the formula it should be like this:

E(Y)=E[E[Y|X]]=[tex]\int[/tex]E[Y|X=x]*[tex]f_{x}[/tex](x)dx

And this is not what they have.....

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# Homework Help: Help with total expectation formula

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