A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a
A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 10E
Related questions
Question
![A uniform distribution is a continuous probability distribution for a random variable x between two values a
and b (a <b), where asxsband all of the values of x are equally likely to occur. The graph of a uniform
distribution is shown to the right. The probability density function of a uniform distribution is shown below.
Show that the probability density function of a uniform distribution satisfies the two conditions for a
probability density function.
1
b-a
1
y=
b-a
Verify the area under the curve is equal to 1. Choose the correct explanation below.
O A. The area under the curve is sum of the maximum and minimum. a + b 0+1=1
OB.
(b-a)
= 1
The area under the curve is two times the mean. 2-
2
OC.
1
The area under the curve is the area of the rectangle. (b-a)
= 1
b-a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdcfa85eb-5a8c-419c-b8e3-0f25acc3fd80%2F0dac4e87-44c2-4bbe-8194-8379486b70c4%2Ffjduuv_processed.png&w=3840&q=75)
Transcribed Image Text:A uniform distribution is a continuous probability distribution for a random variable x between two values a
and b (a <b), where asxsband all of the values of x are equally likely to occur. The graph of a uniform
distribution is shown to the right. The probability density function of a uniform distribution is shown below.
Show that the probability density function of a uniform distribution satisfies the two conditions for a
probability density function.
1
b-a
1
y=
b-a
Verify the area under the curve is equal to 1. Choose the correct explanation below.
O A. The area under the curve is sum of the maximum and minimum. a + b 0+1=1
OB.
(b-a)
= 1
The area under the curve is two times the mean. 2-
2
OC.
1
The area under the curve is the area of the rectangle. (b-a)
= 1
b-a
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