Prove the conditional variance formula [operatorname{Var}(X)=E[operatorname{Var}(X mid Y)]+operatorname{Var}[E(X mid Y)]]

Question:

Prove the conditional variance formula

\[\operatorname{Var}(X)=E[\operatorname{Var}(X \mid Y)]+\operatorname{Var}[E(X \mid Y)]\]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

See More Books

Question Posted: Apr 26, 2024 04:00 PM

See More Questions

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...
A seismic probe bores itself into the seabed, going as deep as it can before running out of fuel. This takes about five minutes. It rotates its spiral drill head at rate R(t) that follows a...
Describe, in detail, how the heapsort algorithm works. [10 marks] Show that the worst-case cost of heapsort is O(n log n). [6 marks] Would it be possible to implement a variant of heapsort based on a...
For the non-seasonal frequencies, use $g \operatorname{lm}()$ to fit the additive exponential model \[ E\left(|\hat{Y}(\omega)|^{2}ight)=\beta_{0}+\beta_{1} \exp \left(-|2 \pi \lambda \omega|^{1 /...
Prove that when carrying costs and restocking costs are as described in the chapter, the EOQ must occur at the point where the carrying costs and restocking costs are equal.
Dextron Manufacturing Company (DMC) was started when it acquired $$60,000$ by issuing common stock. During the first year of operations, the company incurred specifically identifiable product costs...
1. Estimated revenues for the fiscal year were $250,000 and appropriations were $248,000. 2. The tax levy for the fiscal year, of which 99 percent is believed to be collectible, was $200,000. 3....
Prior to the start of fiscal 2013, managers of MultiTech hosted a web conference for its shareholders, financial analysts, and members of the financial press. During the conference, the CEO and CFO...
Problem No. 3 An entity declared property dividend to ordinary shareholders. The property had a carrying amount of P910,000. Fair value on relevant dates: Date of declaration Date of record Date of...
The random edge length $X$ of a cube has a uniform distribution in the interval $[4.8,5.2]$. Determine the correlation coefficient $ho=ho(X, Y)$, where $Y=X^{3}$ is the volume of the cube.
At time $t=0$, a parallel system $S$ consisting of two elements $e_{1}$ and $e_{2}$ starts operating. Their lifetimes $X_{1}$ and $X_{2}$ are dependent with joint survival function...
What basic aspect of superconductivity has prevented its large-scale application thus far?
An epidemiologist plans to conduct a survey to estimate the percentage of women who give birth. How many women must be surveyed in order to be 90% confident that the estimated percentage is in error...
Palmerstown Company established a subsidiary in a foreign country on January 1, Year 1, by investing 8,000,000 pounds when the exchange rate was $1.00/pound. Palmerstown negotiated a bank loan of...
Question 1.Which of the following plans provide the greatest immediate tax benefit for the participating employee? (1) Roth IRA (2) deductible IRA (3) non-deductible IRA (4) 401(k) a. (1) and (3)...
Transcribed image text: 9:13 LTE Done 7 of 7 QUESTION WA AUDION QUESTION 23 = w the tons of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would...
TRUE or FALSE It is 2016 and the D.C. Circuit has issued its ruling in USTA v. FCC . The D.C. Circuit upheld the 2015 Open Internet Order so the FCC's net neutrality rule stands.True or...
Using the frequency distribution table constructed in Exercise 2.19, prepare the cumulative frequency, cumulative relative frequency, and cumulative percentage distributions.
In Problems, solve each system of equations. x + 2y + 3z = 5 y + 11z = 21 5y + 9z = 13
Kirk and Spock formed the Enterprise Company in 2010 as equal owners. Kirk contributed land held an investment ($50,000 basis; $100,000 FMV), and Spock contributed $100,000 cash. The land was used in...
Pedro lives in Puerto Rico and had a net taxable income of $35,000 for the year 20X1. Your gross income totals $60,000. What is Pedro's regular income tax for 20X1? a.$4,620 b.$4,900 c.$2,318 d.$2,520
The change in cash is equal to the change in liabilities less the change in equity plus the change in noncash assets. O True False

Prove the conditional variance formula [operatorname{Var}(X)=E[operatorname{Var}(X mid Y)]+operatorname{Var}[E(X mid Y)]]

Question:

Step by Step Answer:

Applied Probability And Stochastic Processes

Students also viewed these Business questions