Question: Prove by making the substitution u = (x X )/ X in the integrals concerned that the mean and variance of the normal

Prove by making the substitution u = (x – μ_X)/σ_X in the integrals concerned that the mean and variance of the normal distribution are μ_X and σ²_X respectively. (For the variance, integrate u[u exp(–u²/2)] by parts.)

Step by Step Solution

★★★★★

3.37 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

X L27 exp1x 2 24 2 7 1 ue du C ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Modern Engineering Mathematics Questions!

Prove that the method of moments estimators of the mean and variance of a normal distribution are also the M.L.E.s.

X and Y take the value 0 with probability 0.25, the value 1 with probability 0.5, and the value 2 with probability 0.25. Consider independent random variables X and Y with identical probability...

X and Y take the value 0 with probability 0.5 and the value 1 with probability 0.5. Consider independent random variables X and Y with identical probability distributions as given. Let Z = X + X and...

Show the complete solution. Thank you 1. What is the standard error of the mean for a sample size n=35 given the population standard deviation of 30? a. 6.07 b. 5.07 c. 3.0? d. 4.07 2. The average...

please help with the questions A variable is normally distributed with a mean of 100 and a standard deviation of 10. A student wanted to find the percentage of observations of the variable lying...

3. Buses arrive to a bus stop according to an exponential distribution with rate ?= 4 busses/hour. If you arrived at 8:00 am to the bus stop, a) what is the expected time of the next bus? b) Assume...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

Accidental poisoning of children is a great concern to the Poison Control Center. From the past, 12.5% of all children reported with accidental poisoning required hospitalization. For the years 1993...

Number 20: find the variance of X, Var|X| = _________ in terms of P by FIVE ROW METHOD 11) Use the Independence of events A and B to find P[B] = 11) A) 5/9 B) 4/5 C) 3/4 D) 6/11 12) Use Additional...

Horizon Computers manufactures laptops in Germany, Belgium, and Italy. Because of high tariffs between international trade groups, it is sometimes cheaper to ship partially completed laptops to...

1. What is the RMS noise voltage associated with a 10 Q resistor at room temperature when the system has a bandwidth of 5 MHz?

What is the value of each of these prefix expressions? uarr - * * 2 2 * * 1 2 5

A key element of communications for a global company of your choice is maintaining relationships with all its international stakeholders. Identify the various stakeholders and prepare an outline...

Make up a table with columns headed by values of kx running from x = -/2 to x = + in intervals of x of /4 - of course, k = 2/. In each column place the corresponding values of cos (kx - /4) and...

Make up a table with columns headed by values of running from -/2 to 2 in intervals of /4. In each column place the corresponding value of sin , beneath those the values of cos , beneath those the...

Show that for a periodic wave = (2/)v.

1 - Una empresa tiene una nmina bruta de $30.000; impuesto federal sobre la renta retenido de $6,000; impuestos FICA (seguro social) retenidos por $1,860; e impuestos de Medicare retenidos de $435....

Compare the different depreciation methods. Give an example of how companies depreciate their plant assets under each method Please, I want a unique solution that is not copied!!!

Assets (also called property, plant, and equipment) are resources that have physical substance (a definite size and shape), are in the operations of a business, and are not intended for sale to...