Recall that for any function g(X) of a random variable X, where f(x) is the probability density

Question:

Recall that for any function g(X) of a random variable X,

where f(x) is the probability density function of X. Use this result to show that
E(aX + b) = aE(X) + b
and
Var(a X + b) = a2Var(X)

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

Step by Step Answer:

Related Book For book-img-for-question

Probability And Statistics For Engineers And Scientists

ISBN: 9780495107576

3rd Edition

Authors: Anthony Hayter

See More Books

Question Posted: Jun 22, 2016 07:05 AM

See More Questions

Recall that, for any coalition T N, the T-unanimity game (example 1.48) uT GN is Compute the Shapley value of a T-unanimity game. if T cS 0 otherwise
The p.d.f. of a random variable X is f (x) = 2x for 0 x 1. Suppose that measurements are very imprecise, and that all values of X 0.5 are recorded as 0.25 and all values of X > 0.5 are recorded as...
The p.d.f. of a random variable X is f(x) = 1 - x/2 for 0 x 2. Suppose that measurements are very imprecise, and that all values of X 1 are recorded as 0.5 and all values of X > 1 are recorded as...
Requirement 1 Two contribution format statements: current and proposed based on business decision. Requirement 2 For each option current and proposed business decision) calculate the following: a....
What is the difference between a skimming price strategy and a penetration pricing strategy? Under which circumstances is each most likely to be used?
Boehm's Spiral Lifecycle Describe the concept and campare it the Waterfall model(4points) Name the four phase of the spiral cycle and explain them (4points) What is understood by an "alpha-demo"?...
Consider the delivery time data discussed in Example 11.3. Data From Example 11.3 a. Develop a regression model using the prediction data set. b. How do the estimates of the parameters in this model...
You serve as the trustee for the Josephine Frederick testamentary income trust. The trust was created by the will of her late husband, John. Under the terms of John's will, all assets are transferred...
What is the output of the following code? try: print("1") raise ValueError("Yikes") print("2") except TypeError: print("3") except ValueError: print("4") except: print("5"). print("6")
A store maintains data on customers, products and purchase records in three tables: CUSTOMER, PRODUCT, PURCHASE. The store manager wants to know which product is on its maximum discount for each...
Suppose that a temperature has a mean of 1 10 F and a standard deviation of 2.2 F. What are the mean and the standard deviation in degrees Centigrade? (F = 9C/5 + 32)
A person's cholesterol level C can be measured by three different tests. Test-a returns a value Xa with a mean C and a standard deviation 1.2, test- returns a value X with a mean C and a standard...
Do you think hotel companies have segmented the market too much and confused customers? Should hotels keep shifting from hotel product marketing to niche targeting? Why or why not? Today's hotel...
Until a year ago, your business regularly used a local stationery and printing service. They were not that reliable, but you wanted to support a local business. One day, they suddenly informed you...
Are promotional slogans such as Best sushi in town or Atlantas most popular restaurant ethical? Why or why not?
An ethical __________ exists when a person is faced with conflicting but ethical choices or alternatives that are neither entirely right nor entirely wrong; an ethical __________ occurs when a person...
Shari Willison worked as a geologist in your civil engineering firm for 20 years before succumbing to leukemia last week. With only a few dozen employees, the company has always been a tight-knit...
Working as an associate lecturer for a well-known and successful online university, you use your own home as your office. Periodically, you teach residential courses and short, locally based...
The directors of Esplan Ltd have agreed to take over the business owned by Rakesh on 1. March 2015. Rakesh plans to retire. Both businesses operate as retailers of electrical goods. The summarised...
The value of a share of common stock depends on the cash flows it is expected to provide, and those flows consist of the dividends the investor receives each year while holding the stock and the...
Gary Schwartz is the top salesman for his company. Records indicate that he makes a sale on 70% of his sales calls. If he calls on four potential clients, what is the probability that he makes...
If 10% of all disk drives produced on an assembly line are defective, what is the probability that there will be exactly one defect in a random sample of 5 of these? What is the probability that...
Trowbridge Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out of control....
Can social norms be understood as emergent properties of social interactions, reflecting negotiated agreements among members of a society regarding acceptable behavior and moral standards?
A quantitative portfolio manager is very good at managing against the Russell 2000 Index. In fact, she is expected to achieve an B of 0.5% per month. Unfortunately, her benchmark is the S&P 500. She...
Suppose that a QEPM department hires a new quantitative equity portfolio manager to manage one of its portfolios. Suppose that the portfolio managers benchmark is the S&P 500, with a Sharpe ratio of...

Recall that for any function g(X) of a random variable X, where f(x) is the probability density

Question:

E(g(X))= | g(x)f(x)dx

Step by Step Answer:

E aX b aE X b Var aX b ...View the full answer

Probability And Statistics For Engineers And Scientists

Students also viewed these Statistics questions