Let be a standard normal random variable z, and let be a differentiable function with derivative g'.

Question:

a. Show that E[g'(Z)] = E(Zg(Z)];

b. Show that E[Zⁿ⁺¹] = nE[Z^n-1].

c. Find E[Z⁴].

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

Let X be a standard normal random variable (i. e., X ~ N ( 0,1)). Find the PDF of Y= |X|. If the transformation is 0, s0
Let X be a standard normal random variable (i. e., X ~ N ( 0,1)). Find the PDF of Y= |X|.
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. a. P(0 Z 2.17) b. P(0 Z 1) c. P(-2.50 Z 0) d. P(-2.50 Z 2.50) e....
What are some techniques of good writers? Which ones do you use regularly?
Given this equilibrium, predict the direction of shift for each stress listed. Co2(g) + C(s) + 171kJ + 2CO (g) a. Addition of CO b. Increased pressure c. Addition of a catalyst
Why did convertible arbitrage strategies perform so poorly in 2008?
The current in a cylindrical solenoid is increased smoothly from $I_{\mathrm{i}}=0.40 \mathrm{~A}$ at $t_{\mathrm{i}}=3.0 \mathrm{~s}$ to $I_{\mathrm{f}}=1.20 \mathrm{~A}$ at...
Use the data in Exercise to prepare an income statement and the current assets section of the balance sheet for each company. Ignore income taxes. In Exercise Using the following data, compute (1)...
Answer the question by showing the calculation procedure. Verified the answer by using the MATLAB coding. Submit all the answers (calculation procedure & MATLAB code) to MS Team. For all of the...
The proposed rates were not in the range the CEO expected given the pricing analysis. The CEO has asked the pricing actuary to verify the total projected loss cost excluding potential large storm...
A bus travels between the two cities and which are 100 miles apart. If the bus has a breakdown, the distance from the breakdown to city has a uniform distribution over (0, 100). There is a bus...
Let be a random variable that takes on values between 0 and c. That is, P{0 X c} = 1. Show that Var(X) c 2 /4
Invoice price of goods is $5,000. Purchase terms are 2/10, n/30 and the invoice is paid in the week of receipt. The shipping terms are FOB shipping point, and the shipping costs amount to $200. What...
The questions below should be calculated based on the following assumptions (which will be the same for questions 14-17) : The band Thrice consists of four members: Dustin Kensrue, Teppei Teranishi,...
The 80/20 principle in fashion means that: Group of answer choices 80% of your sales will be the most important product the smallest portion of product styles will lead to the largest portion of...
DomCo, a domestic corporation, is a wholly-owned subsidiary of its Japanese parent corporation, ASIAco, which manufactures lightbulbs. During the current year, DomCo pays $100 million for 100 million...
Use these materials: Use the "Sources of Law" section of the Lau & Johnson (pages. 14-22) This is the website for "Sources of Law"...
1. What would I find on a job-cost sheet; please give examples? 2. In your own words explain to your classmates what Job Costing is. 3. Explain a job-order costing system and give examples? 4. What...
The catalytic hydrogenation of 0.5 g of a hydrocarbon at 25 C consumed about 200 mL of H2 under 1 atm of pressure. Reaction of the hydrocarbon with ozone, followed by treatment with hydrogen peroxide...
Nitrogen monoxide reacts with hydrogen as follows: 2NO(g)+ H2(g) N2O(g) + H2O(g) The rate law is [H2]/ t = k[NO]2[H2], where k is 1.10 107 L2/(mol2s) at 826oC. A vessel contains NO and H2 at...
Use the result that, for a nonnegative random variable Y, to show that, for a nonnegative random variable X, and make the change of variables t = xn. E[Y] = P{Y > t} dt
Let X be a random variable that takes on values between 0 and c. That is, P{0 X c} = 1. Show that Var(X) c2/4 One approach is to first argue that E[X2] cE[X] and then use this inequality to show...
Show that Z is a standard normal random variable, then, for x > 0, (a) P{Z > x} = P{Z < x}; (b) P{|Z| > x} = 2P{Z > x}; (c) P{|Z| < x} = 2P{Z < x} 1.
Operating exposure arises from unexpected changes in the future value of operations and financing cash flows, as a result of unexpected changes in the exchange rate. Discuss (with examples) the two...
Internet of Things (IoT) is defined as "the interconnection via the Internet of computing devices embedded in everyday objects, enabling them to send and receive data". A. Briefly explain Bluetooth...
Using the class Turtle and recursion write java code to draw the following shape

Let be a standard normal random variable z, and let be a differentiable function with derivative g'.

Question:

Step by Step Answer:

a To show that EgZ EZgZ we can use the chain rule of calculus By the chain rule we have ...View the full answer

A First Course In Probability

Students also viewed these Mathematics questions