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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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Find the variance and standard deviation of the distribution shown in the table. Then graph the distribution.

Random variable, x 0 1 2 3 4
Frequency of x, n(x) 1 2 4 2 1

To determine

To calculate: The Variance and the standard deviation of the distribution shown below:

Random variable (x) 0 1 2 3 4
Frequency of x, n(x) 1 2 4 2 1

And also graph the distribution:

Explanation

Given Information:

The distribution shown below:

Random variable (x) 0 1 2 3 4
Frequency of x, n(x) 1 2 4 2 1

Formula Used:

The variance is given by,

V(x)=ab(xμ)2f(x)dxorV(x)=abx2f(x)dxμ2

The standard deviation of x is,

σ=V(x)

Calculation:

Consider the table,

Random variable (x) 0 1 2 3 4
Frequency of x, n(x) 1 2 4 2 1

For the expected value,

E(x)=0(110)+1(210)+2(410)+3(

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