Chapter 9.2, Problem 27E

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

Finding a Probability A probability density function is defined over the interval [0, 8]. The probability that x lies in [0, 3] is 0.8. What is the probability that x lies in [3, 8]?

To determine

To calculate: The probability that x lies between [3,8] if a probability density function is defined over the interval [0,8] and probability that x lies between [0,3] is 0.8.

Explanation

Given Information:

Probability density function is defined over [0,8] and probability that x lies between [0,3] is 0.8.

Formula used:

If f(x) is probability density function and it is defined over [0,a] so;

0af(x)dx=1

If for some other interval [0,b] probability is P then;

0af(x)dx=10bf(x)dx+baf(x)dx=1P+baf(x)dx=1baf(x)dx=1P

Calculation:

It is given that,

Probability density function is defined over [0,8] and probability that x lies between [0,3] is 0

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