If the random variable X has the mean and the standard deviation s, show that the random variable Z whose values are related to those of X by means of the equation z x has E(Z) 0 and var(Z) 1 A distribution that has the mean 0 and the variance 1 is said to be in standard form, and when we perform the above change of variable, we are said to be standardizing the distribution of X

Question: If the random variable X has the mean and the standard deviation s, show that the random variable Z whose values are related to

If the random variable X has the mean µ and the standard deviation s, show that the random variable Z whose values are related to those of X by means of the equation z = x- µ / σ has E(Z) = 0 and var(Z) = 1
A that has the mean 0 and the variance 1 is said to be in standard form, and when we perform the above change of variable, we are said to be standardizing the of X.

Step by Step Solution

★★★★★

3.40 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

x 4 E x Ex 0 ... 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

Document Format (1 attachment)

583-S-J-P-D (718).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

The random variable X has the following distribution. a. Find the mean and variance for the probability distribution below. b. Determine the probability distribution of Y where Y = 5X. c. Use the...

If the random variable X has a t-distribution with v degrees of freedom, explain why the random variable Y = X2 has an F-distribution with degrees of freedom 1 and v.

The random variable x has a normal distribution with = 300 and = 30. a. Find the probability that x assumes a value more than two standard deviations from its mean. More than three standard...

Please complete in less than one hour. do not accept if you can not deliver. Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientic...

Page 21 of 25 Previous Next Given a non-standard normal random variable (X) with the mean 97 and standard deviation 23, find X = a when the area between 97 and a is 0.4589. Separate the answer with...

Given a non-standard normal random variable (X) with the mean 100 and standard deviation 15. find X = a when the area between 100 and a is 0.4484. Table for required value of : Separate the answer...

A random variable has normal distribution mean 40 and standard deviation 4. Show how you would do the following with R code. a) Determine and interpret the quartiles of this variable. b) Find the...

For the following problem, you will need formulas for binomial experiments. n = the number of independent trials x = the number of successes in n trials 5 = success F = fail p = P(S) = probability of...

18. A quality inspector picks a sample of 15 items at random from a manufacturing process known to produce 10% defective items. Let X be the number of defective items found in the random sample of 15...

A coin is thrown three times, and interest is in the number, X, of heads resulting. (a) Find the probability function of the random variable X. (b) Find the mean and standard deviation of the random...

Natasha's Flowers, a local florist, purchases fresh flowers each day at the local flower market. The buyer has a budget of $985 per day to spend. Different flowers have different profit margins, and...

Pharma Shop Ltd. was a mid-sized public company that had been in operation for many years. On December 31, 2010, it had an unlimited number of common shares authorized and 5,200,000 shares issued at...

Eleanor submitted a claim under her insurance policy that was rejected by the insurer. After reviewing the policy, her attorney indicated that the policy language relating to the coverage was...

In a closed economy, aggregate saving can only increase if aggregate investment expenditure also increases.

Proactine, a new medicine for acne, is claimed by the manufacturer to be 80% effective. It is applied to the affected area of a sample of 15 people. What is the probability that: a. All 15 will show...

Customers at the Bank of Commerce of Idaho Falls, Idaho, default at a rate of .005 on small home-improvement loans. The bank has approved 400 small home-improvement loans. Assuming the Poisson...

A study of the attendance at the University of Alabamas basketball games revealed that the distribution of attendance is normally distributed with a mean of 10,000 and a standard deviation of 2,000....

by matlab a medicine tablet stip; design an algorithm to detect and count the number of missing pills.

The current spot rate of dollars per pound as quoted in a newspaper is ________ or ________. Use the table to answer the following question(s). Yen: Spot and Forward(/$)Pound: Spot and Forward ($/)...

Suppose you are a corporate Treasurer and you need to finance a $100 investment with a borrowing for 5 years. Your choices are a floating rate loan at the default free spot rate, currently at 0.01,...