   Chapter 9.3, Problem 5CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

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

# Find the expected value and standard deviation of the uniform probability density function f ( x ) 1 2 ,  0 ≤ x ≤ 2 .

To determine

To calculate: The expected value and standard deviation of the uniform probability density function f(x)=12 on the interval 0x2.

Explanation

Given information:

The function is,

f(x)=12

And the interval is 0x2.

Formula used:

To find the expected value or mean of x,

μ=E(x)=abxf(x)dx

The variance of x is,

V(x)=abx2f(x)dxμ2

The standard deviation of x is,

σ=V(x)

Where, f is a probability density function with a continuous random variable x in the interval [a,b]

Calculation:

Consider the provided function is,

f(x)=12

Now apply the formula μ=E(x)=abxf(x)dx to find the expected value,

μ=0212xdx=[x22]02==1

Now draw the function f(x)=12 by using ti-83 calculator,

Step1: Press ON key.

Step2: Press “Y=” key.

Step3: Enter the equation “Y=1/2” before Y1.

Step4: Set the window as,

Xmax=5,Xmin=5,Xscl=0

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