   Chapter 9.2, Problem 23E ### 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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# Finding a Probability In Exercises 19-26, sketch the graph of the probability density function over the indicated interval and find each probability. See Example 3. f ( x ) = 3 16 x ,        [ 0 , 4 ] (a) P ( 0 < x < 2 ) (b) P ( 2 < x < 4 ) (c) P ( 1 < x < 3 ) (d) P ( x ≤ 3 )

(a)

To determine

To calculate: The probability P(0<x<2) over the interval [0,4], where the probability density function is f(x)=316x.

Explanation

Given Information:

The probability density function is f(x)=316x and the interval is [0,4].

Formula used:

A function f is a probability density function when it is non-negative and continuous on the interval [a,b] and when abf(x)dx=1 and the probability,

P(a<x<b)=abf(x)dx

Calculation:

Consider the function,

f(x)=316x

Now, the probability that x lies between 0 and 2 is computed as

P(0<x<2)=02f(x)dx=02316xdx=316

(b)

To determine

To calculate: The probability P(2<x<4) over the interval [0,4], where the probability density function is f(x)=316x.

(c)

To determine

To calculate: The probability P(1<x<3) over the interval [0,4], where the probability density function is f(x)=316x.

(d)

To determine

To calculate: The probability P(x3) over the interval [0,4], where the probability density function is f(x)=316x.

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