Refer to Exercise 5.149.a Find E(Y2

Chapter 5, Problem 150SE

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QUESTION:

Refer to Exercise .
a Find \(E\left(Y_{2} \mid Y_{1}=y_{1}\right)\).
b Use Theorem
 to find \(E\left(Y_{2}\right)\).
c Find \(E\left(Y_{2}\right)\) directly from the marginal density of \(Y_{2}\).

Equation Transcription:

Text Transcription:

E(Y_2|Y_1=y_1)

E(Y_2)

E(Y_2)

Y_2

Questions & Answers

QUESTION:

Refer to Exercise .
a Find \(E\left(Y_{2} \mid Y_{1}=y_{1}\right)\).
b Use Theorem
 to find \(E\left(Y_{2}\right)\).
c Find \(E\left(Y_{2}\right)\) directly from the marginal density of \(Y_{2}\).

Equation Transcription:

Text Transcription:

E(Y_2|Y_1=y_1)

E(Y_2)

E(Y_2)

Y_2

ANSWER:

Solution:

Step 1 of 3:

Let Y1 and Y2 have a joint density function given by,

           

We have to find,

  1. E(Y2/Y1=y1).
  2. E(Y2).
  3. E(Y2) by using the marginal density of Y2.

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