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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Show that f ( x ) = 1 2 x is a probability density function over the interval [0, 2].

To determine

To prove: The given function f(x)=x2 is probability density function over the given range [0,2].

Explanation

Given Information:

The given function is f(x)=x2 and range is [0,2].

Formula Used:

If the f(x) is function over the interval [a,b]. Than the density function satisfies the given condition as,

abf(x)=1

Proof:

Consider the given function,

Now, apply the formula,

02f(x)dx=02x2dx=12[x22]02=44

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