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MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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
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 a ≤x≤b
and 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.
y =
Verify the area under the curve is equal to 1. Choose the correct explanation below.
A.
1
b-a
O B.
The area under the curve is the area of the rectangle. (b-a)
(b-a)
2
OC. The area under the curve is sum of the maximum and minimum. a+b=0+1=1
The area
the curve
times the mean. 2-
(b-a)=
= 1
= 1
1.
b-a
Show that the value of the function can never be negative. Choose the correct explanation below.
O A. The numerator of the probability density function is 1, so the function must always be positive.
OB. The denominator of the probability density function is always positive because a <b, so b-a>0, therefore the function must always be positive.
OC. The value of b - a is less than one, therefore the value of the function must always be greater than 1.
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