   Chapter 8.5, Problem 3E

Chapter
Section
Textbook Problem

Let f (x) = 30x2(1 − x)2 for 0 ≤ x ≤ 1 and f (x) = 0 for all other values of x. (a) Verify that f is a probability density function. (b) Find P ( X ≤ 1 3 ) .

(a)

To determine

To verify: The function f is a probability density function.

Explanation

Given information:

The function f(x)=30x2(1x)2 for 0x1 .

The function f(x)=0 for all other values of x.

Hence, f(x)0 for all x.

The region lies between a=0 and b=1 .

Show the function as follows:

f(x)=30x2(1x)2 (1)

Modify Equation (1).

f(x)=30x2(1+x22x)=30x2+30x460x3=30x460x3+30x2

Apply probability density function as follows:

(A) The probability density function f of a random variable X satisfies the condition f(x)0 for all x

(b)

To determine

To calculate: The value of P(X13) .

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

let f(x) = x 1, g(x) = x+1, and h(x) = 2x3 1. Find the rule for each function. 17. f-hg

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Differentiate. A(v)=v2/3(2v2+1v2)

Calculus (MindTap Course List)

Prove that limx21x=12.

Single Variable Calculus

Write the formula for the trade discount rate. (7-5)

Contemporary Mathematics for Business & Consumers

True or False: dmdv stands for the derivative of the function m with respect to the variable v.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The equation of the tangent plane to for is:

Study Guide for Stewart's Multivariable Calculus, 8th 