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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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A probability density function is defined over the interval [0, 4]. The probability that x lies in [0. 1] is 0.6. What is the probability that x lies in [1, 4]?

To determine

To calculate: The probability for the x lies in the interval [1,4] if probability density function in interval [0,1] is 0.6.

Explanation

Given Information:

The defined probability density function in interval [1,4].

Formula used:

Consider a function f of a continuous random variable x whose set of values is the interval

[a,b]. The probability density on the interval be related to a variable x, which lies in the interval [a,b].

Then the probability density on the interval [a,b] as defined as cdf(x)dx=1.

The probability that x lies in the interval [c,d] is given by P(cxd)=df(x)dx

where acb.

Calculation:

Consider the primary equation,

04f(x)dx=1

Consider the secondary equation,

01f(x)dx=0.6

And the ternary equation, 04f(x)dx=01f(x)dx+14f(x)dx

Substitute the value of 01f(x)dx=0

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