Chapter 4: Q167SE (page 281)

Identify the type of continuous random variable—uniform,normal, or exponential—described by each of the following probability density functions:
a. $f (x) = \frac{e^{- \frac{x}{7}}}{7}; x > o$
b. $f (x) = \frac{1}{20}; 5 < x < 25$
c. $f (x) = \frac{e^{- . 5 {[(x - 10) / 5]}^{2}}}{5 \sqrt{2 π}}$

Short Answer

Expert verified

X is an exponential random variable.
X is a uniform random variable.
X is a normal random variable.

Step by step solution

Given information

X is arandom variable.

Identifying the random variable when f(x)=e-x77;x>o

$f (x) = \frac{e^{- \frac{x}{7}}}{7}; x > o = \frac{1}{θ} e^{- \frac{x}{θ}}$

Where, $θ = 7$ and $x > 0$

The p.d.f of an exponential distribution is $f (x) = = \frac{1}{θ} e^{- \frac{x}{θ}}; x > o$

Hence, X is an exponential random variable.

Identifying the random variable when f(x)=120;5<x<25

$f (x) = \frac{1}{20}; 5 < x < 25 = \frac{1}{25 - 5} = \frac{1}{d - c}$

Where, d= 25 and c = 5

The p.d.f of uniform distribution is $f (x) = \frac{1}{d - c}; c \leq x \leq d$

Hence, X is a uniform random variable.

Identifying the random variable when f(x)=e-.5[(x-10)/5]252π

$f (x) = \frac{e^{- . 5 {[(x - 10) / 5]}^{2}}}{5 \sqrt{2 π}} = \frac{1}{σ \sqrt{2 π}} e^{- \frac{1}{2} {[(x - μ) / σ]}^{2}}$

Where , $μ = 10$ and $σ = 5$

The p.d.f of uniform distribution is $f (x) = \frac{1}{σ \sqrt{2 π}} e^{- \frac{1}{2} {[(x - μ) / σ]}^{2}}$

Hence, X is a normal random variable.

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Identify the type of continuous random variable—uniform,normal, or exponential—described by each of the following probability density functions:
a. $f (x) = \frac{e^{- \frac{x}{7}}}{7}; x > o$
b. $f (x) = \frac{1}{20}; 5 < x < 25$
c. $f (x) = \frac{e^{- . 5 {[(x - 10) / 5]}^{2}}}{5 \sqrt{2 π}}$

Short Answer

Step by step solution

Given information

Identifying the random variable when f(x)=e-x77;x>o

Identifying the random variable when f(x)=120;5<x<25

Identifying the random variable when f(x)=e-.5[(x-10)/5]252π

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Identify the type of continuous random variable—uniform,normal, or exponential—described by each of the following probability density functions:a.f(x)=e-x77;x>ob.f(x)=120;5<x<25c.f(x)=e-.5[x-10/5]252π

Short Answer

Step by step solution

Given information

Identifying the random variable when f(x)=e-x77;x>o

Identifying the random variable when f(x)=120;5<x<25

Identifying the random variable when f(x)=e-.5[(x-10)/5]252π

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

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Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.