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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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Demand Repeat Exercise 47 for the probability density function

f ( x ) = 3 256 ( x 2 ) ( 10 x ) , [ 2 , 10 ] .

(a)

To determine

To calculate: The mean and standard deviation of the given probability density function f(x)=3256(x2)(10x) with range [2,10].

Explanation

Given Information:

The probability density function:

f(x)=3256(x2)(10x) with range [2,10]

Formula used:

If  f(x) is a Probability density function with range [a,b].

Mean:

µ=abxf(x)dx  

Variance:

V=abx2f(x)dxµ2  

Standard Deviation:

σ =V

Calculation:

Consider given probability density function:

f(x)=3256(x2)(10x)      with range 

(b)

To determine

To calculate: The median of the given probability density function

f(x)=3256(x2)(10x) with range [2,10].

(c)

To determine

To calculate: The probability for given probability density function

f(x)=3256(x2)(10x) with range [2,10].

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