(9) When X, Y have a bivariate normal density with respective means ux, µy, respective variables o, oy andcorrelation p, we haveρσχE(X|Y = y) = µx+(y – uy),OyVar(X|Y = y) = o(1 – p²).Verify the theorem of total expectation (TTE).The following verifications are proposed.(a) Since Var(X|Y = y) = oz(1 – p²) does not depend on y, therefore, the TTE holds.(b) Since E(X|Y = y) depends only on y, the TTE holds.(c) Since E(X|Y) = µx+Pox* (Y – µy), we see that E(E(X|Y)) = µx =E(X). Therefore, the TTE holds.oy(d) TTE does not hold.(e) None of the aboveThe correct verification is(a)(b)(c)(d)(e)N/A(Select One)

The theorem of total expectation(TTE) is given by E(X) = E(E(X|Y))

Answered: Verify the theorem of total expectation…

Math

Probability

Verify the theorem of total expectation (TTE).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

(9) When X, Y have a bivariate normal density with respective means ux, µy, respective variables o, oy and
correlation p, we have
ρσχ
E(X|Y = y) = µx+
(y – uy),
Oy
Var(X|Y = y) = o(1 – p²).
Verify the theorem of total expectation (TTE).
The following verifications are proposed.
(a) Since Var(X|Y = y) = oz(1 – p²) does not depend on y, therefore, the TTE holds.
(b) Since E(X|Y = y) depends only on y, the TTE holds.
(c) Since E(X|Y) = µx+
Pox
* (Y – µy), we see that E(E(X|Y)) = µx =
E(X). Therefore, the TTE holds.
oy
(d) TTE does not hold.
(e) None of the above
The correct verification is
(a)
(b)
(c)
(d)
(e)
N/A
(Select One)

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