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Introduction to Econometrics 3rd Edition by James Stock, James Stock
النسخة 3الرقم المعياري الدولي: 978-9352863501Introduction to Econometrics 3rd Edition by James Stock, James Stock
النسخة 3الرقم المعياري الدولي: 978-9352863501 تمرين 2
Consider three random variables X, Y, and Z. Suppose that Y takes on k values Y₁ ,…, y k that X takes on l values X₁;..., x l , and that Z takes on m values Z 1 ,...,z m. The joint probability distribution of X, Y , Z is Pr( X = x , Y = y, Z = z ), and the conditional probability distribution of Y given X and Z is ![Consider three random variables X, Y, and Z. Suppose that Y takes on k values Y₁ ,…, y k that X takes on l values X₁;..., x l , and that Z takes on m values Z 1 ,...,z m. The joint probability distribution of X, Y , Z is Pr( X = x , Y = y, Z = z ), and the conditional probability distribution of Y given X and Z is a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution. b. Show that E ( Y ) = E [ E ( Y | X, Z)].](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3cf3_9e5f_bf3e_478438e935bd_SM2686_00.jpg)
a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution.
b. Show that E ( Y ) = E [ E ( Y | X, Z)].![Consider three random variables X, Y, and Z. Suppose that Y takes on k values Y₁ ,…, y k that X takes on l values X₁;..., x l , and that Z takes on m values Z 1 ,...,z m. The joint probability distribution of X, Y , Z is Pr( X = x , Y = y, Z = z ), and the conditional probability distribution of Y given X and Z is a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution. b. Show that E ( Y ) = E [ E ( Y | X, Z)].](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3cf3_9e60_bf3e_c9bd59cbd9a4_SM2686_00.jpg)
![Consider three random variables X, Y, and Z. Suppose that Y takes on k values Y₁ ,…, y k that X takes on l values X₁;..., x l , and that Z takes on m values Z 1 ,...,z m. The joint probability distribution of X, Y , Z is Pr( X = x , Y = y, Z = z ), and the conditional probability distribution of Y given X and Z is a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution. b. Show that E ( Y ) = E [ E ( Y | X, Z)].](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3cf3_9e61_bf3e_d762e5351427_SM2686_00.jpg)
![Consider three random variables X, Y, and Z. Suppose that Y takes on k values Y₁ ,…, y k that X takes on l values X₁;..., x l , and that Z takes on m values Z 1 ,...,z m. The joint probability distribution of X, Y , Z is Pr( X = x , Y = y, Z = z ), and the conditional probability distribution of Y given X and Z is a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution. b. Show that E ( Y ) = E [ E ( Y | X, Z)].](https://d2lvgg3v3hfg70.cloudfront.net/SM2686/11eb9b5b_3cf3_c572_bf3e_1395c0d23fcb_SM2686_00.jpg)
a. Explain how the marginal probability that Y = y can be calculated from the joint probability distribution.
b. Show that E ( Y ) = E [ E ( Y | X, Z)].
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We are asked to consider three random va...
Introduction to Econometrics 3rd Edition by James Stock, James Stock
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