(9) When X, Y have a bivariate normal density with respective means µx, µy, respective variables o7, o7 and correlation p, we haveE(X|Y = y) = Hx+ρσχ(y – HY),Var(X|Y = y) = o(1 – p²).σΥVerify the theorem of total expectation (TTE).The following verifications are proposed.(a) Since Var(X|Y = y) = ož(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.(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 is stated as E(X) = E(E(X|Y = y)

Answered: Verify the theorem of total expectation…

Math

Probability

Verify the theorem of total expectation (TTE).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.4: Derivatives Of Exponential Functions

Problem 53E

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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.

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(9) When X, Y have a bivariate normal density with respective means µx, µy, respective variables o7, o7 and correlation p, we have
E(X|Y = y) = Hx+
ρσχ
(y – HY),
Var(X|Y = y) = o(1 – p²).
σΥ
Verify the theorem of total expectation (TTE).
The following verifications are proposed.
(a) Since Var(X|Y = y) = ož(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.
(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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