Chapter 9.3, Problem 30E

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

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Special Probability Density Functions In Exercises 29-34, identify the probability density function. Then find the mean, variance, and standard deviation without integrating. f ( x ) = 1 6 , [ 0 , 6 ]

To determine

To calculate: The mean variance and standard deviation without integrating of the probability density functions f(x)=16.

Explanation

Given Information:

The probability density function is:

f(x)=16

Where, the interval of function is [0,6].

Formula used:

The formula for uniform probability density function is defined as:

f(x)=1ba,axb

This probability density function represents a continuous random variable for which each outcome is equally likely.

Formula used to find the mean of probability density function is

μ=a+b2, where μ is mean and formula used to find variance of probability density is v(x)=(ba)212 and standard deviation σ=(ba)12 or σ=v(x).

Calculation:

Consider the given equation

f(x)=16;x[0,6].

Compare [0,6] with [a,b]

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