Explanation Given: The function is f ( x ) = 2 x 2 and the interval is [ 1 , 2 ] . Definition used: The function f is a probability density function of a random variable X in the interval [ a , b ] if, 1. f ( x ) ≥ 0 for all x in the interval [ a , b ] . 2. ∫ a b f ( x ) d x = 1 Calculation: First, note that condition 1 holds, that is, f ( x ) ≥ 0 for the interval [ 1 , 2 ] . Next show that condition 2 holds. ∫ 1 2 f ( x ) d x = ∫ 1 2 2 x 2 d x = 2 ∫ 1 2 x − 2 d x = 2 [ x − 2 + 1 − 2 + 1 ] 1 2 ( ∵ ∫ x n d x = x n + 1 n + 1 + C ) = − 2 [ x − 1 ] 1 2 On further simplification the above expression becomes, ∫ 1 2 f ( x ) d x

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Question

Chapter 18.1, Problem 1YT

To determine

To show: The function f(x)=2x2 is the probability density function on [1,2] and find the probability that X will be between 32 and 2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17, Problem 106RE

Chapter 18.1, Problem 2YT

Students have asked these similar questions

How to verify that this is function is a probability density function? Also, how would you find P(x<3) Let f(x) = { pi/10 sin (pix/5) if 0<x<5 0 if x<0 or x>5

A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density function

Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [1, 5]

Chapter 18 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 18.1 - Prob. 1YT Ch. 18.1 - Prob. 2YT Ch. 18.1 - Using the probability density function of Example...Ch. 18.1 - Use part (a) of Example 5 to calculate the...Ch. 18.1 - Evaluate each of the following integrals. (Sec....Ch. 18.1 - Prob. 2WE Ch. 18.1 - Prob. 3WE Ch. 18.1 - Decide whether the functions defined as follows...Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E

Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E Ch. 18.1 - Prob. 6E Ch. 18.1 - Prob. 7E Ch. 18.1 - Prob. 8E Ch. 18.1 - Prob. 9E Ch. 18.1 - Prob. 10E Ch. 18.1 - Prob. 11E Ch. 18.1 - Prob. 12E Ch. 18.1 - Prob. 13E Ch. 18.1 - Prob. 14E Ch. 18.1 - Prob. 15E Ch. 18.1 - Prob. 16E Ch. 18.1 - Prob. 17E Ch. 18.1 - Prob. 18E Ch. 18.1 - Prob. 19E Ch. 18.1 - Prob. 20E Ch. 18.1 - Prob. 21E Ch. 18.1 - Find the cumulative distribution function for the...Ch. 18.1 - Prob. 23E Ch. 18.1 - Prob. 24E Ch. 18.1 - Prob. 25E Ch. 18.1 - Prob. 26E Ch. 18.1 - Prob. 27E Ch. 18.1 - Prob. 28E Ch. 18.1 - Prob. 29E Ch. 18.1 - Prob. 30E Ch. 18.1 - Prob. 31E Ch. 18.1 - Prob. 32E Ch. 18.1 - Prob. 33E Ch. 18.1 - Prob. 34E Ch. 18.1 - Life Span of a Computer Part The life (in months)...Ch. 18.1 - Prob. 36E Ch. 18.1 - Prob. 37E Ch. 18.1 - Prob. 38E Ch. 18.1 - Prob. 39E Ch. 18.1 - Prob. 40E Ch. 18.1 - Prob. 41E Ch. 18.1 - Flea Beetles The mobility of an insect is an...Ch. 18.1 - Prob. 43E Ch. 18.1 - Prob. 44E Ch. 18.1 - Prob. 45E Ch. 18.1 - Earthquakes The time between major earthquakes in...Ch. 18.1 - Earthquakes The time between major earthquakes in...Ch. 18.1 - Prob. 48E Ch. 18.1 - Driving Fatalities We saw in a review exercise in...Ch. 18.1 - Prob. 50E Ch. 18.1 - Time of Traffic Fatality The National Highway...Ch. 18.2 - Repeat Example l for the probability density...Ch. 18.2 - Prob. 2YT Ch. 18.2 - Prob. 3YT Ch. 18.2 - Find P(1 X 2) for each probability function on...Ch. 18.2 - Prob. 2WE Ch. 18.2 - Prob. 1E Ch. 18.2 - Prob. 2E Ch. 18.2 - Prob. 3E Ch. 18.2 - Prob. 4E Ch. 18.2 - Prob. 5E Ch. 18.2 - Prob. 6E Ch. 18.2 - Prob. 7E Ch. 18.2 - In Exercises 18, a probability density function of...Ch. 18.2 - Prob. 9E Ch. 18.2 - Prob. 10E Ch. 18.2 - Prob. 11E Ch. 18.2 - Prob. 12E Ch. 18.2 - Prob. 13E Ch. 18.2 - Prob. 14E Ch. 18.2 - Prob. 15E Ch. 18.2 - Prob. 16E Ch. 18.2 - Prob. 17E Ch. 18.2 - For Exercises 1520, (a) find the median of the...Ch. 18.2 - Prob. 19E Ch. 18.2 - Prob. 20E Ch. 18.2 - Prob. 21E Ch. 18.2 - Prob. 22E Ch. 18.2 - Prob. 23E Ch. 18.2 - Prob. 24E Ch. 18.2 - Prob. 25E Ch. 18.2 - Prob. 26E Ch. 18.2 - Losses After Deductible A manufacturers annual...Ch. 18.2 - Prob. 28E Ch. 18.2 - Prob. 29E Ch. 18.2 - Prob. 30E Ch. 18.2 - Prob. 31E Ch. 18.2 - Prob. 32E Ch. 18.2 - Petal Length The length (in centimeters) of a...Ch. 18.2 - Prob. 34E Ch. 18.2 - Prob. 35E Ch. 18.2 - Prob. 36E Ch. 18.2 - Prob. 37E Ch. 18.2 - Prob. 38E Ch. 18.2 - Annual Rainfall The annual rainfall in a remote...Ch. 18.2 - Prob. 40E Ch. 18.2 - Prob. 41E Ch. 18.2 - Prob. 42E Ch. 18.2 - Time of Traffic Fatality In Exercise 51 of the...Ch. 18.3 - Prob. 1YT Ch. 18.3 - Prob. 2YT Ch. 18.3 - Prob. 3YT Ch. 18.3 - Prob. 1WE Ch. 18.3 - Prob. 2WE Ch. 18.3 - Prob. 1E Ch. 18.3 - Prob. 2E Ch. 18.3 - Find (a) the mean of the distribution, (b) the...Ch. 18.3 - Prob. 4E Ch. 18.3 - Prob. 5E Ch. 18.3 - Prob. 6E Ch. 18.3 - Prob. 7E Ch. 18.3 - Prob. 8E Ch. 18.3 - Prob. 9E Ch. 18.3 - Prob. 10E Ch. 18.3 - Prob. 11E Ch. 18.3 - Prob. 12E Ch. 18.3 - Prob. 13E Ch. 18.3 - Prob. 14E Ch. 18.3 - Prob. 15E Ch. 18.3 - Prob. 16E Ch. 18.3 - Prob. 17E Ch. 18.3 - Prob. 18E Ch. 18.3 - Prob. 19E Ch. 18.3 - Prob. 20E Ch. 18.3 - Prob. 21E Ch. 18.3 - Prob. 22E Ch. 18.3 - Prob. 23E Ch. 18.3 - Prob. 24E Ch. 18.3 - Prob. 25E Ch. 18.3 - Prob. 26E Ch. 18.3 - Prob. 27E Ch. 18.3 - Prob. 28E Ch. 18.3 - Prob. 29E Ch. 18.3 - Prob. 30E Ch. 18.3 - Prob. 31E Ch. 18.3 - Prob. 32E Ch. 18.3 - Prob. 33E Ch. 18.3 - Prob. 34E Ch. 18.3 - Insured Loss An insurance policy is written to...Ch. 18.3 - Prob. 36E Ch. 18.3 - Printer Failure The lifetime of a printer costing...Ch. 18.3 - Prob. 38E Ch. 18.3 - Prob. 39E Ch. 18.3 - Prob. 40E Ch. 18.3 - Prob. 41E Ch. 18.3 - Prob. 42E Ch. 18.3 - Finding Prey H. R. Pulliam found that the time (in...Ch. 18.3 - Life Expectancy According to the National Center...Ch. 18.3 - Prob. 45E Ch. 18.3 - Prob. 46E Ch. 18.3 - Prob. 47E Ch. 18.3 - Prob. 48E Ch. 18.3 - Prob. 49E Ch. 18.3 - Prob. 50E Ch. 18.3 - Prob. 51E Ch. 18.3 - Prob. 52E Ch. 18.3 - Prob. 53E Ch. 18.3 - Prob. 54E Ch. 18 - Prob. 1RE Ch. 18 - Prob. 2RE Ch. 18 - Prob. 3RE Ch. 18 - Prob. 4RE Ch. 18 - Prob. 5RE Ch. 18 - Prob. 6RE Ch. 18 - Prob. 7RE Ch. 18 - Prob. 8RE Ch. 18 - Prob. 9RE Ch. 18 - Prob. 10RE Ch. 18 - Prob. 11RE Ch. 18 - Prob. 12RE Ch. 18 - Prob. 13RE Ch. 18 - Prob. 14RE Ch. 18 - Prob. 15RE Ch. 18 - Prob. 16RE Ch. 18 - Prob. 17RE Ch. 18 - Prob. 18RE Ch. 18 - Prob. 19RE Ch. 18 - Prob. 20RE Ch. 18 - Prob. 21RE Ch. 18 - Prob. 22RE Ch. 18 - Prob. 23RE Ch. 18 - Prob. 24RE Ch. 18 - Prob. 25RE Ch. 18 - Prob. 26RE Ch. 18 - Prob. 27RE Ch. 18 - Prob. 28RE Ch. 18 - Prob. 29RE Ch. 18 - Prob. 30RE Ch. 18 - Prob. 31RE Ch. 18 - Prob. 32RE Ch. 18 - Prob. 33RE Ch. 18 - Prob. 34RE Ch. 18 - Prob. 35RE Ch. 18 - Prob. 36RE Ch. 18 - Prob. 37RE Ch. 18 - Prob. 38RE Ch. 18 - Prob. 39RE Ch. 18 - Prob. 40RE Ch. 18 - Prob. 41RE Ch. 18 - Prob. 42RE Ch. 18 - Prob. 43RE Ch. 18 - Prob. 44RE Ch. 18 - Prob. 45RE Ch. 18 - Prob. 46RE Ch. 18 - Prob. 47RE Ch. 18 - Prob. 48RE Ch. 18 - Prob. 49RE Ch. 18 - Prob. 50RE Ch. 18 - Prob. 51RE Ch. 18 - Prob. 52RE Ch. 18 - Prob. 53RE Ch. 18 - Prob. 54RE Ch. 18 - Prob. 55RE Ch. 18 - Prob. 56RE Ch. 18 - Prob. 57RE Ch. 18 - Prob. 58RE Ch. 18 - Prob. 59RE Ch. 18 - Prob. 60RE Ch. 18 - Prob. 61RE Ch. 18 - Prob. 62RE

Knowledge Booster

The function f ( x ) = 2 x 2 is the probability density function on [ 1 , 2 ] and find the probability that X will be between 3 2 and 2.

Solution Summary: The author explains that the function f(x)=2x is the probability density function of a random variable X in the interval

To show: The function f(x)=2x2 is the probability density function on [1,2] and find the probability that X will be between 32 and 2.

Want to see the full answer?

Chapter 18 Solutions