   Chapter 9.3, Problem 29E ### 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
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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 10 , [ 0 , 10 ]

To determine

To calculate: The mean variance and standard deviation of the probability distribution functions f(x)=110.

Explanation

Given Information:

The probability distribution function is,

f(x)=110

Where the interval of function is [0,11].

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)=110interval[0,10]

Compare [0,10] with [a,b]

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