Explanation Given information: f ( x ) = 1 2 x , 1 ≤ x ≤ 4 . Formula used: Let X be a continuous random variable, whose possible values lie between A and B , and f ( x ) be the probability density function for X . Then, the expected value (average) of X is the number E ( X ) defined by, E ( X ) = ∫ A B x f ( x ) d x . And the variance of X is defined by, Var ( X ) = ∫ A B x 2 f ( x ) d x − ( E ( X ) ) 2 . Calculation: Let X be the continuous random variable with values between A = 1 and B = 4 with density function, f ( x ) = 1 2 x By using the formula of expected value, E ( X ) = ∫ 1 4 x f ( x ) d x = ∫ 1 4 x 1 2 x d x . = 1 2 ∫ 1 4 x x − 1 / 2 d x = 1 2 ∫ 1 4 x 1 / 2 d x = 1 2 ( 2 3 x 3 / 2 ) | 1 4

15th Edition

ISBN: 9780137590438

Author: Goldstein

Publisher: PEARSON

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 12.3, Problem 1CYU

To determine

To calculate: The expected value and variance of the random variable X whose density function is f(x)=12x, 1≤x≤4.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.2, Problem 38E

Chapter 12.3, Problem 2CYU

Students have asked these similar questions

For the system consisting of the lines: and 71 = (-8,5,6) + t(4, −5,3) 72 = (0, −24,9) + u(−1, 6, −3) a) State whether the two lines are parallel or not and justify your answer. b) Find the point of intersection, if possible, and classify the system based on the number of points of intersection and how the lines are related. Show a complete solution process.

3. [-/2 Points] DETAILS MY NOTES SESSCALCET2 7.4.013. Find the exact length of the curve. y = In(sec x), 0 ≤ x ≤ π/4

H.w WI M Wz A Sindax Sind dy max Утах at 0.75m from A w=6KN/M L=2 W2=9 KN/m P= 10 KN B Make the solution handwritten and not artificial intelligence because I will give a bad rating if you solve it with artificial intelligence

Chapter 12 Solutions

CALCULUS+ITS APPLICATIONS-MYMATHLAB

Ch. 12.1 - Compute the expected value and the variance of the...Ch. 12.1 - Prob. 2CYU Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Probability Table, Expected Value The number of...Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E

Ch. 12.1 - Decision Making Based on Expected Value A citrus...Ch. 12.1 - Prob. 10E Ch. 12.2 - Prob. 1CYU Ch. 12.2 - Prob. 2CYU Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - An experiment consists of selecting a point at...Ch. 12.2 - Prob. 28E Ch. 12.2 - Prob. 29E Ch. 12.2 - Prob. 30E Ch. 12.2 - Prob. 31E Ch. 12.2 - Prob. 32E Ch. 12.2 - Prob. 33E Ch. 12.2 - Prob. 34E Ch. 12.2 - Prob. 35E Ch. 12.2 - A random variable X has a cumulative distribution...Ch. 12.2 - Prob. 37E Ch. 12.2 - Prob. 38E Ch. 12.3 - Prob. 1CYU Ch. 12.3 - Prob. 2CYU Ch. 12.3 - Prob. 1E Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Prob. 5E Ch. 12.3 - Prob. 6E Ch. 12.3 - Prob. 7E Ch. 12.3 - Prob. 8E Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.3 - Prob. 12E Ch. 12.3 - Expected Reading Time The amount oftime (in...Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - If X is a random variable with density function...Ch. 12.3 - Prob. 20E Ch. 12.3 - Prob. 21E Ch. 12.3 - Prob. 22E Ch. 12.3 - Prob. 23E Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.4 - The emergency flasher on an automobile is...Ch. 12.4 - Prob. 2CYU Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - In a large factory there is an average of two...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Reliability of Electronic Components Suppose that...Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 17E Ch. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 19E Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Prob. 22E Ch. 12.4 - Prob. 23E Ch. 12.4 - Prob. 24E Ch. 12.4 - Prob. 25E Ch. 12.4 - Normal Distribution and Life of a Tire Suppose...Ch. 12.4 - Amount of Milk in a Container If the amount of...Ch. 12.4 - Breaking weight Theamount of weight required to...Ch. 12.4 - Time of a commute A student with an eight oclock...Ch. 12.4 - Prob. 30E Ch. 12.4 - Diameter of a Bolt A certain type of bolt must fit...Ch. 12.4 - Prob. 32E Ch. 12.4 - Prob. 33E Ch. 12.4 - Prob. 34E Ch. 12.4 - Prob. 35E Ch. 12.4 - Prob. 36E Ch. 12.4 - Prob. 37E Ch. 12.5 - A public health officer is tracking down the...Ch. 12.5 - Suppose that a random variable X has a Poisson...Ch. 12.5 - Prob. 2E Ch. 12.5 - Prob. 3E Ch. 12.5 - Prob. 4E Ch. 12.5 - Number of Insurance Claims The monthly number of...Ch. 12.5 - Waiting Time in an Emergency Room On a typical...Ch. 12.5 - Prob. 7E Ch. 12.5 - Number of Cars at a Tollgate During a certain part...Ch. 12.5 - Poisson Distribution in a Mixing Problem A bakery...Ch. 12.5 - Prob. 10E Ch. 12.5 - Prob. 11E Ch. 12.5 - Quality Control The quality-control department at...Ch. 12.5 - Two Competing Companies In a certain town, there...Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - Prob. 19E Ch. 12.5 - Prob. 20E Ch. 12.5 - Prob. 21E Ch. 12.5 - Prob. 22E Ch. 12.5 - Prob. 23E Ch. 12.5 - Prob. 24E Ch. 12.5 - Prob. 25E Ch. 12.5 - The number of accidents occurring each month at a...Ch. 12 - What is probability table?Ch. 12 - Prob. 2FCCE Ch. 12 - Prob. 3FCCE Ch. 12 - Prob. 4FCCE Ch. 12 - Prob. 5FCCE Ch. 12 - Prob. 6FCCE Ch. 12 - Prob. 7FCCE Ch. 12 - Prob. 8FCCE Ch. 12 - Prob. 9FCCE Ch. 12 - Give two ways to compute the variance of a...Ch. 12 - Prob. 11FCCE Ch. 12 - Prob. 12FCCE Ch. 12 - Prob. 13FCCE Ch. 12 - Prob. 14FCCE Ch. 12 - How is an integral involving a normal density...Ch. 12 - Prob. 16FCCE Ch. 12 - Prob. 17FCCE Ch. 12 - Let X be a continuous random variable on 0x2, with...Ch. 12 - Prob. 2RE Ch. 12 - Prob. 3RE Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Probability of Gasoline Sales A certain gas...Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 15RE Ch. 12 - Prob. 16RE Ch. 12 - Prob. 17RE Ch. 12 - Deciding on a Service Contract The condenser motor...Ch. 12 - Prob. 19RE Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE Ch. 12 - Area under the Normal Curve It is useful in some...Ch. 12 - Prob. 28RE Ch. 12 - Prob. 29RE Ch. 12 - Prob. 30RE Ch. 12 - Prob. 31RE Ch. 12 - Prob. 32RE Ch. 12 - Prob. 33RE Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The expected value and variance of the random variable X whose density function is f ( x ) = 1 2 x , 1 ≤ x ≤ 4 .

Solution Summary: The author explains the formula used to calculate the expected value and variance of the random variable X.

Concept explainers

Videos

To calculate: The expected value and variance of the random variable X whose density function is f(x)=12x, 1≤x≤4.

Want to see the full answer?

Chapter 12 Solutions