   Chapter 9.3, Problem 6SWU ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 5 and 6, find each probability using the given probability density function. f ( x ) = 6 x − 6 x 2 , [ 0 , 1 ] (a) P ( x ≤ 1 2 ) (b) P ( 1 4 ≤ x 3 4 )

(a)

To determine

To calculate: The probability P(x12) of the probability density function f(x)=6x6x2, [0,1].

Explanation

Given information:

The function is,

f(x)=6x6x2, [0,1]

Formula used:

To find the probability,

P(axb)=abf(x)dx

Where, f is a probability density function with a continuous random variable x in the interval [a,b]

Calculation:

Consider the provided function is,

f(x)=6x6x2

Now apply the formula P(axb)=abf(x)dx to find the probability,

P(axb)=ab(6x6x2)dx=ab(6x)dxab(6x2)dx=[6(x22)]ab[6(x33)]ab=[3x2]ab[2x3]ab

Further solve,

P(axb)=[3x2]ab

(b)

To determine

To calculate: The probability P(14x34) of the probability density function f(x)=6x6x2, [0,1].

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