Prove that [E(g(X)Y|X] = g(X)E[Y|X].

Question:

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

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Probability

ISBN: 9780134753119

10th Edition

Authors: Sheldon Ross

See More Books

Question Posted: Sep 09, 2021 03:09 AM

See More Questions

Prove that if the joint cdf of X and Y satisfies Fx,y(x,y) = FX(X)FY(y), then for any pair of intervals (a, b), and (c, d), P(a < X < b, c < Y < d) = P(a < X < b)P(c < Y < d).
Prove that v = x + i y and v- = x - i y are linearly independent complex vectors if and only if their real and imaginary parts x and y are linearly independent real vectors.
Prove that if x and y are real numbers, then max(x, y) + min(x, y) = x + y. Use a proof by cases, with the two cases corresponding to x y and x < y, respectively.
In the early part of 2013, the partners of Page, Childers, and Smith sought assistance from a local accountant. They had begun a new business in 2012 but had never used an accountants services. Page...
N atoms can have a wide range of oxidation numbers. Assign oxidation numbers for the N atom in each compound, all of which are known compounds. a. N2O5 b. N2O4 c. NO2 d. NO e. N2H4 f. NH3
Many companies acquire software to help them monitor and control their costs and as an aid to their accounting systems. One company that supplies such software is proDacapo (prodacapo.com). There are...
5. Pop Corporation sells an inventory item to its subsidiary, Son Company, to be used as a plant asset by Son. The workpaper entry to eliminate intercompany profits in the year of sale will not...
For Briggs Company actual sales are $1,200,000 and break-even sales are $900,000. Compute (a) The margin of safety in dollars and (b) The margin of safety ratio.
Gemini Inc. operates a goods store that caters for government, private individuals, and organizations. The company has three service departments and two operating departments. Data on the five...
In a subway station, there are exactly enough customers on the platform to fill three trains. The arrival time of the nth train is X1+ + Xn where X1, X2 . . . are iid exponential random variables...
Prove that if E[Y|X = x] = E[Y] for all x, then and are uncorrelated; give a counterexample to show that the converse is not true.
Show that if X and Y are independent, then E[X| Y = y] = E[X] for all y a. In the discrete case; b. In the continuous case.
For the given test statistic, sample sizes and significance levels, state whether you would reject or not reject the null hypothesis. a. Test statistic = 1.96, n = 10, 5% one-tailed b. Test statistic...
Air at $1 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$ flows in a 4-cm-diameter glass pipe at a velocity of $7 \mathrm{~m} / \mathrm{s}$. The friction factor for this flow is (a) 0.0266 (b)...
Find the regime of the boundary layer at the location of $0.1 \mathrm{~m}$ from the leading edge of an aerofoil, if the airspeed is $80 \mathrm{~ms}^{-1}$, and air condition is at that of sea...
``Nuclear Deterrence,'' by Harvey A . Smith, UMAP327. The author analyzes the stability of the arms race, assuming objectives similar to those suggested by General Taylor. The module develops...
A saturated vapor feed at $1000.0 \mathrm{kmol} / \mathrm{h}$ of methanol $(5.0 \mathrm{~mol} \%)$ and water $(95.0 \mathrm{~mol} \%)$ is fed to a distillation column with 18 stages plus a...
Use the partition functions in Equations 1.98, 1.99, and 1.100 to find the translational, rotational, and vibrational contributions to the average energy of a diatomic molecule. Compare each result...
Firm L had net assets at the end of the year of $730,000. The only transactions affecting stockholders equity during the year were net income of $154,000 and dividends of $94,000. Required: Calculate...
Assume a simple Keynesian depression economy with a multiplier of 4 and an initial equilibrium income of $3,000. Saving and investment equal $400, and assume full employment income is $4,000. a. What...
(a) A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; when he flips it, it shows heads. What is the probability that it is the fair coin? (b)...
Urn A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a...
In Example 3a, what is the probability that someone has an accident in the second year given that he or she had no accidents in the first year?
*please calculate irr in excel
Which of the following would not be a period cost? Research and development Direct materials Office supplies Advertising costs
\ table [ [ Activity Cost Pool,Activity Measure,Total Cost,Total Activity ] , [ Machining , Machine - hours,$ 3 3 0 , 0 0 0 , 1 5 , 0 0 0 MHs ] , [ Machine setups,Number of setups,$ 3 0 0 , 0 0 0 , 5...

Prove that [E(g(X)Y|X] = g(X)E[Y|X].

Question:

Step by Step Answer:

Proof Let X and Y be two random variables and let gX be a function of X We want to ...View the full answer

A First Course In Probability

Students also viewed these Mathematics questions