Expectation of two phase process
- Thread starter mrolnik
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Steven G
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What are your thoughts!? What have you tried? Where are you stuck? This is a math help forum where we help students solve their problem. It is quite hard to help you if you show us no work at all. If you had read the forum's posting guidelines and followed them you would have been helped by now.
let [MATH]Z[/MATH] be a random variable whose value is [MATH]\Sigma_{i=0}^{X}Y[/MATH] ([MATH]X[/MATH] is evaluated once)
let [MATH]Z_i[/MATH] be a random variable whose value is the outcome of the [MATH]i[/MATH]s game in the described process then [MATH]Z=\Sigma_{i}{Z_i}[/MATH][MATH]P_{Z_i}(z)=\Sigma_{j}P(Y=z, X=j)=\Sigma_{j}{P(Y=z/X=j)}{P_{X}(j)}=P_{Y}(z)P_{X}(\ge i)[/MATH][MATH]E(Z_i)=\Sigma_{z}zP_{Y}(z)P_{X}(\ge i)=P_{X}(\ge i)E(Y)[/MATH][MATH]E(Z)=\Sigma_{i}E(Z_i)=\Sigma_{i}P_{X}(\ge i)E(Y)=E(Y)\Sigma_{i}P_{X}(\ge i)[/MATH]
[MATH]E(Z)=E(Y)\Sigma_{i}P_{X}(\ge i)[/MATH] does not feel right to me.
let [MATH]Z_i[/MATH] be a random variable whose value is the outcome of the [MATH]i[/MATH]s game in the described process then [MATH]Z=\Sigma_{i}{Z_i}[/MATH][MATH]P_{Z_i}(z)=\Sigma_{j}P(Y=z, X=j)=\Sigma_{j}{P(Y=z/X=j)}{P_{X}(j)}=P_{Y}(z)P_{X}(\ge i)[/MATH][MATH]E(Z_i)=\Sigma_{z}zP_{Y}(z)P_{X}(\ge i)=P_{X}(\ge i)E(Y)[/MATH][MATH]E(Z)=\Sigma_{i}E(Z_i)=\Sigma_{i}P_{X}(\ge i)E(Y)=E(Y)\Sigma_{i}P_{X}(\ge i)[/MATH]
[MATH]E(Z)=E(Y)\Sigma_{i}P_{X}(\ge i)[/MATH] does not feel right to me.